GIFT  OF 


Mathematics  Dept 


ESSAYS    ON    THE    LIFE 
AND  WORK  OF  NEWTON 


SIR  ISAAC  NEWTON. 


LIFE  AND  WORK  OF 
NEWTON 


BY 

AUGUSTUS   DE   MORGAN 

EDITED,    WITH   NOTES    AND   APPENDICES,    BY 

PHILIP   E.  B.  JOURDAIN 

M.  A.  (Cantab.) 


CHICAGO  AND   LONDON 
THE  OPEN  COURT  PUBLISHING  COMPANY 

1914 


Copyright  in  Great  Britain  under  the  Act  of  191 1 


EDITOR'S  PREFACE 

AUGUSTUS  DE  MORGAN'S  biographical  sketch  en- 
titled ' '  Newton  "  appeared  in  The  Cabinet  Portrait 
Gallery  of  British  Worthies^  in  1846,  and  is  the 
first  essay  printed  in  the  present  volume.  It  was, 
as  Mrs  De  Morgan2  said,  "  after  Baily's  Life  of 
Flamsteed*  the  first  English  work  in  which  the 
weak  side  of  Newton's  character  was  made  known. 
Justice  to  Leibniz,  to  Flamsteed,  even  to  Whiston, 
called  for  this  exposure  ;  and  the  belief  that  it  was 
necessary  did  not  lower  the  biographer's  estimate 
of  Newton's  scientific  greatness,  and  of  the  simplicity 
and  purity  of  his  moral  character.  Francis  Baily's 
discovery  of  the  correspondence  between  the  Rev. 
John  Flamsteed,  the  first  Astronomer  Royal,  and 
Abraham  Sharp,  as  well  as  between  Newton, 
Halley,  and  Flamsteed,  on  the  publication  of  Flam- 
steed's  catalogue  of  stars,  had  thrown  a  new  light 

1  Vol.  xi,  London,  1846,  pp.  78-117.  This  series  was  edited  by 
Charles  Knight.  A  three-columned  quarto  edition  in  one  volume,  and 
giving  no  editorial  credit,  was  published  in  London  by  Henry  G.  Bohn 
in  1853  under.the  title  Old  England's  Worthies :  A  Gallery  of  Portraits. 
Besides  the  small  woodcut  portraits,  it  contains  twelve  full-page 
"  illuminated  engravings."  De  Morgan's  "  Newton  "  occupies  pp.  220- 
224  of  this  edition. 

*  Memoir  of  Augustus  De  Morgan,  London,  1882,  p.  256. 

3  London,  1835. 

v 

609758 


vi  EDITOR'S 

on  the  character  of  Newton.  It  appeared  that  the 
practical  astronomer  had  been  treated  ungenerously 
by  Newton,  who  failed  to  observe  the  conditions  of 
publication  agreed  to  by  all  parties  ;  and  afterwards, 
when  remonstrated  with,  omitted  the  name  of 
Flamsteed  in  places  where  it  had  formerly  stood  in 
the  earlier  editions  of  the  Principia. " 

"  My  husband,"  adds  Mrs  De  Morgan,  "entered 
into  the  enquiry  with  keen  interest,  and  with  a 
power  of  research  possible  only  to  one  who  was 
fully  master  of  the  history  of  mathematical  dis- 
covery. "  And  it  is  not  only  mathematical  discovery 
and  controversy  that  De  Morgan  treats  in  the  just, 
broad-minded,  and  high-minded  way  that  is  char- 
acteristic of  him.  He  disclaimed  any  particular 
interest  in  those  religious  beliefs  of  Newton  which 
he  discussed  so  thoroughly  ;  still,  "  notwithstanding 
this  disclaimer,"  says  Mrs  De  Morgan,1  "I  believe 
my  husband  felt  more  interest  in  the  question,  from 
its  own  nature,  than  he  was  himself  aware  of. 
Whether  I  am  mistaken  in  this  may  be  surmised 
by  those  who  have  read  his  own  letter  to  his  mother 
in  this  volume.2  He  says,  '  Whatever  Newton's 
opinions  were,  they  were  the  result  of  a  love  of 
truth,  and  of  a  cautious  and  deliberate  search  after 

1  Op.  cit.,  p.  260.     Cf.  pp.  260-261,  and  §  XI.  of  the  first  essay 
printed  below. 

2  This  letter  of  De  Morgan's  to  his  mother,  which  is  printed  in  the 
Memoir,  is  on  pp.   139-144  and  there  is  no  mention  of  Newton  in 
it.      The  passage,  however,  occurs  towards  the  end  of  §  XI.  of  De 
Morgan's  biography  of  Newton  printed  below. 


PREFACE  vii 

it.'  That  Newton  was  a  firm  believer  in  Christianity 
as  a  revelation  from  God  is  very  certain,  but  whether 
he  held  the  opinions  of  the  majority  of  Christians 
on  the  points  which  distinguish  Trinitarians  from 
Arians,  Socinians,  and  Humanitarians,  is  the 
question  of  controversy." 

The  second  of  De  Morgan's  Essays  printed  in 
this  volume  concerns  the  great  controversy  about 
the  invention  of  the  fluxional  or  infinitesimal  calculus, 
in  which  Newton  and  Leibniz  were  the  principals. 
The  essay  printed  is  from  the  Companion  to  the 
Almanac -,  and  is  now  extremely  rare.  It  is  of 
great  interest  and  importance  both  on  account  of 
the  fairness  and  vigour  which  De  Morgan  always 
showed  in  the  defence  of  Leibniz  against  the  im- 
putations of  Newton  and  the  Royal  Society,  and 
because  it  first  introduced  the  English  public  to 
Gerhardt's  important  discovery  of  Leibniz's  manu- 
scripts showing  his  gradual  discovery  of  the  calculus 
in  1673-1677.  This  essay  also  contains  a  summary 
of  much  of  De  Morgan's  historical  work  on  the  con- 
troversy./ In  January  1846,  a  paper  by  De  Morgan, 
"On  a  point  connected  with  the  Dispute  between 
Keill  and  Leibnitz  about  the  Invention  of  Fluxions," 
was  read  to  the  Royal  Society,  and  it  was  after- 
wards printed  in  the  Philosophical  Transactions^ 

1  Phil.  Trans.)  1846,  pp.  107-109.  This  paper  was  wrongly  stated 
in  Mrs  De  Morgan's  Memoir  (pp.  257,  402,  406)  to  be  printed  in  the 
Transactions  of  the  Cambridge  Philosophical  Society.  On  the  subject 
of  this  paper,  see  the  second  appendix  to  the  third  essay. 


x  EDITOR'S 

planatory,  or  critical  nature  have  been  added  to  all 
the  essays,  but  all  that  is  not  De  Morgan's  is  put 
in  square  brackets.  Such  notes  have  become 
necessary,  and  it  is  hoped  that  the  present  ones 
will  reply  to  all  the  calls  of  necessity  and  will  make 
the  book  both  useful  and  complete.  Very  little 
has  to  be  criticised  in  De  Morgan's  history  or  con- 
clusions. Like  everything  he  wrote,  these  essays 
of  his  are  marked  by  scrupulous  care,  sanity  of 
judgment,  and  wide  reading  ;  and  one  hardly  knows 
which  to  admire  most :  the  breadth  or  the  height  of 
his  mind. 

Several  minor  structural  alterations  have  been 
made  :  the  first  and  third  essays  have  been  split 
into  sections  to  facilitate  reading  and  reference ; 
the  names  of  Huygens  and  Leibniz  have  through- 
out had  their  spelling  altered  from  "  Huyghens  " 
and  ' '  Leibnitz  "  except  in  the  titles  of  books  and 
actual  quotations.1  Leibniz  always  signed  himself 
as  "Leibniz,"  but  I  have  always  cited  the  titles 
of  books  as  they  were  printed,  even  though  mis- 
spellings may  have  occurred  there.  This  seems 
quite  indispensable  for  convenience  in  reference. 

The  frontispiece  is  from  an  engraving  by  E. 
Scriven  of  Vanderbank's  portrait  of  Newton  in  the 
possession  of  the  Royal  Society  of  London.  An 
engraving  from  this  picture  accompanied  the  original 

1  The  spelling  "  Leibnitz  "  even  in  titles  of  books  where  "  Leibniz" 
is  written  is  one  of  the  faults  in  Gray's  Bibliography. 


PREFACE  xi 

of  De  Morgan's  biographical  sketch  ;  but  the  present 
frontispiece  is  from  a  much  finer  engraving  prefixed 
to  the  biography  of  Newton  in  the  first  volume  of 
The  Gallery  of  Portraits  :  with  Memoirs.  * 

PHILIP  E.  B.  JOURDAIN. 

THE  LODGE, 

GIRTON,  CAMBRIDGE, 

ENGLAND. 

1  London,  1833,  pp.  79-88.  On  the  portraits  of  Newton,  cf.  Samuel 
Crompton,  Proc.  Lit.  and  Phil.  Soc.  of  Manchester,  vol.  vi,  1866-7, 
pp.  1-7. 


CONTENTS 

TAGZ 

EDITOR'S  PREFACE  ......       v 

I.  NEWTON  (1846)  .....       i 

II.  A  SHORT  ACCOUNT  OF  SOME  RECENT  DISCOVERIES 
IN  ENGLAND  AND  GERMANY  RELATING  TO 
THE  CONTROVERSY  ON  THE  INVENTION 
OF  FLUXIONS  (1852)  .  .  .  .65 

APPENDIX  ON  THE  MANUSCRIPTS  AND  PUBLICA- 
TIONS OF  NEWTON  AND  LEIBNIZ  .  .  102 

III.  REVIEW  OF  BREWSTER'S  MEMOES  OF  THE  LIFE, 
WRITINGS,  AND  DISCOVERIES  OF  SIR  ISAAC 
NEWTON  (1855)  .  .  .  .  .117 

APPENDIX  I.— DE  MORGAN'S  VIEW  OF  LEIBNIZ'S 
CHARACTER  .  .  .  .  .183 

APPENDIX  II.— NOTE  BY  DE  MORGAN  ON  THE 
CHARACTER  OF  NEWTON  AND  ON  THE  ACTIONS 
OF  THE  ROYAL  SOCIETY,  WRITTEN  IN  1858  .  187 

INDEX  .......    194 


xiii 


I 

NEWTON 

(1846) 


NEWTON 

A  BIOGRAPHY  of  Newton,  intended  for  such  a  collec- 
tion as  this,  must  necessarily  be  much  condensed  ; 
the  account  of  his  discoveries  must  be-  little  more 
than  allusion,  and  a  perfect  list  of  his  writings  and 
their  editions  is  out  of  the  question.  The  only  Life 
which  exists  on  any  considerable  scale  (as  justly 
remarked  by  the  author)  is  that  by  Sir  David 
Brewster  in  the  "Family  Library"  (No.  24):  this 
will  be  our  chief  reference  on  matters  of  fact.1  On 

1  [The  fullest  life  of  Newton  that  has  appeared  was  published  after 
this  biography  (1846)  by  De  Morgan,  and  was  also  written  by  Sir 
David  Brewster  under  the  title  Memoirs  of  the  Life,  Writings,  and 
Discoveries  of  Sir  Isaac  Newton,  2  vols.,  Edinburgh,  1855.  A  second 
edition — apparently  unaltered,  even  as  to  the  mistakes — was  issued  at 
Edinburgh  in  1860.  De  Morgan's  famous  but  scarce  review  (1855)  of 
this  work  is  reprinted  below  as  the  third  of  these  Essays.  An  ex- 
tremely valuable  "  Synoptical  View  of  Newton's  Life"  was  prefixed  to 
J.  Edleston's  Correspondence  of  Sir  Isaac  Newton  and  Professor  Cotes, 
.  .  .  (London  and  Cambridge,  1850).  The  earlier  biographies  of 
Newton  were  as  follows:  J.  B.  Biot,  "Newton,"  Biographic  Univer- 


of  Si 

Library,"  No.  24,  1831  (revised  by  W.  T.  Lynn  in  1875)  ;  De  Morgan, 
"Newton,"  Penny  Cyclopedia,  1840;  Fontenelle's  Eloge  de  Monsieur 
le  Chevalier  Newton,  1728,  translated  into  English  in  the  same  year; 
and  Benjamin  Martin  in  Biographia  Philosophica,  1764.  For  bio- 
graphies of  Newton,  see  also  G.  J.  Gray,  A  Bibliography  of  the  Works 
of  Sir  Isaac  Newton,  Cambridge,  second  edition,  1907  (the  first  was 
published  in  1888),  pp.  70-76. 

Various  aspects  of  Newton's  work   have   been   dealt   with  in,  for 

3 


4  NB  iVTON 

those  of  opinion,  particularly  as  to  the  social  char- 
acter of  Newton,  we  must  differ  in  some  degree 
from  our  guide,  as  well  as  from  all  those  (no  small 
number)  whose  well-founded  veneration  for  the 
greatest  of  philosophical  inquirers  has  led  them  to 
regard  him  as  an  exhibition  of  goodness  all  but 
perfect,  and  judgment  unimpeachable.  That  we  can 
follow  them  a  long  way  will  sufficiently  appear  in 
the  course  of  this  sketch. 

I 

Isaac  Newton  was  born  at  Woolsthorpe,  near 
Grantham,  in  Lincolnshire,  on  Christmas  Day, 
1642  :l  a  weakly  and  diminutive  infant,  of  whom  it 
is  related  that,  at  his  birth,  he  might  have  found 
room  in  a  quart  mug.  He  died  on  March  the  2Oth, 
1727,  after  more  than  eighty-four  years  of  more 
than  average  bodily  health  and  vigour  ;  it  is  a  proper 
pendant  to  the  story  of  the  quart  mug  to  state  that 
he  never  lost  more  than  one  of  his  second  teeth. 
His  father,  Isaac  Newton,  though  lord  of  the  poor 

example,  (i)  Stephen  Peter  Rigaud,  Historical  Essay  on  the  First 
Publication  of  Sir  Isaac  Newton's  Principia,  Oxford,  1838  ;  (2)  W.  W. 
Rouse  Ball,  An  Essay  on  Newton's  "  Principia,"  London  and  New 
York,  1893 ;  (3)  Ferdinand  Rosenberger,  Isaac  Newton  und  seine 
physikalischen  Principien^  .  .  .  Leipsic,  1895.  Besides  these,  there 
is  notably  the  account  and  critique  of  Newton's  principles  of  mechanics 
in  Ernst  Mach's  Mechanik,  translated  into  English  by  T.  J.  M'Cormack 
under  the  title  The  Science  of  Mechanics :  A  Critical  and  Historical 
Account  of  its  Development,  third  edition,  Chicago,  1907,  pp.  201-245.] 
1  [Old  style.  The  new  year  was  then  reckoned  from  March  the  25th, 
so  that  what  we  now  call,  for  example,  January  the  6th,  1672,  was  then 
January  the  6th,  1671,  and  is  sometimes  written  "January  the  6th, 
1671/2."  We  will  always  write  dates  in  the  modern  way.] 


NE  WTON  5 

manor  of  Woolsthorpe,  was  in  fact  a  small  farmer, 
who  died  before  the  birth  of  his  son.  The  manor, 
which  had  been  in  the  family  about  a  hundred 
years,  was  Newton's  patrimony :  it  descended  to 
the  grandson  of  his  father's  brother.  This  heir  sold 
it  in  1732  to  Edmund  Tumor,  to  whose  descendant 
the  world  is  much  indebted  for  a  collection  of  facts 
connected  with  Newton's  history.1  A  curious  tradi- 
tion of  a  conversation  of  Newton  with  Gregory,  in 
which  the  former  affirmed  himself  to  be  descended 
from  a  Scotch  family,  his  grandfather  having  come 
from  East  Lothian  at  the  accession  of  James  I., 
will  be  found  in  the  appendix  to  Brewster's  Life? 
with  a  careful  attempt  to  see  how  far  the  presump- 
tion it  affords  can  be  supported  by  collateral  evidence. 
But  Newton  himself  (twenty  years  before  the  date 
of  this  conversation)  gave  his  pedigree  on  oath  into 
the  Heralds'  Office,  stating  that  he  had  reason  to 
believe  that  his  great  grandfather's  father  was  John 
Newton,  of  West  by,  in  Lincolnshire.3  To  bring  all 
that  relates  to  his  family  together,  his  mother,  when 
he  was  three  years  old,  married  Barnabas  Smith, 
rector  of  North  Witham,  by  whom  she  had  one  son 
and  two  daughters  (who  gained  by  marriage  the 


1  [Edmund  Tumor,  Collections  for  the  History  of  the  Town  and  Soke 
of  Grant  ham,  containing  authentic  Memoirs  of  Sir  /.  Newton  now  first 
published,  1806.     This  book  contains,  among  other  things,  Conduitt's 
sketch  of  Newton  which  was  drawn  up  for  the  use  of  Fontenelle.] 

2  \Cf.  Brewster's  Memoirs,  1855,  vol.  ii,  pp.  537-545.] 

3  [On  Newton's  pedigree  (1705),  see  Tumor,  op.  cit.,  p.   169,  and 
the  reference  to  Brewster's  Memoirs  given  in  the  fourth  note.] 


6  NE  WTON 

names  of  Pilkington  and  Barton).  The  children  of 
these  three,  four  nephews  and  four  nieces  of  Newton 
by  the  half-blood,  inherited  his  personal  property, 
amounting  to  £32,000.  One  of  these  nieces, 
Catherine,  who  married  a  Colonel  Barton,  became  a 
widow,  and  afterwards  lived  in  Newton's  house. 
After  her  second  marriage  (to  Mr  Conduitt,  who 
succeeded  Newton  as  master  of  the  Mint),  she  and 
her  husband  resided  with  him  until  his  death.1  They 
are  the  authority  for  many  anecdotes  given  by 
Fontenelle  in  the  Eloge  read  to  the  Academy  of 
Science.  Mrs  Conduitt's  only  daughter,  Catherine, 
married  Mr  Wallop,  afterwards  Viscount  Lymington 
by  inheritance  ;  she  transmitted  a  large  collection 
of  Newton's  papers,  also  by  inheritance,  to  the 
family  of  the  Earl  of  Portsmouth.  These  "  Ports- 
mouth Papers"  still  exist  unpublished,2  and  there 
is  also  a  mass  of  papers  in  the  Library  of  Trinity 
College,  Cambridge,  which  are  well  known.3 

1  [It   is  a  mistake   that  Catherine  Barton,  the  daughter  of  Robert 
Barton  and    Hannah  Smith,  Newton's   half-sister,   was  the   widow   of 
Colonel  Barton.     That  this  was  so  was  stated  in  an  anonymous  Life  of 
the  Earl  of  Halifax  published  in  1715.     Cf.  Brewster,  Memoirs^  1855, 
vol.  ii,  p.  273.] 

2  [The  scientific  part  of  the  "  Portsmouth  Papers"  was  presented  by 
Lord  Portsmouth  to  the  University  of  Cambridge,  and  has  now  been 
classified    and    deposited   in   the    University  Library.     A  descriptive 
catalogue  of  it  was  published  at  Cambridge,  in  1888,  under  the  title 
A   Catalogue  of  the  Portsmouth  collection  of  Books  and  Papers  written 
by  or  belonging  to  Sir  Isaac  Newton,  the  Scientific  Portion  of  which 
has  been  presented  by  the  Earl  of  Portsmouth  to   the    University  of 
Cambridge.     This  catalogue  was  drawn  up  by  the  Syndicate  appointed 
on  November  the  6th,  1872,  and  the  Preface  was  signed  by  H.  R.  Luard, 
G.  G.  Stokes,  J.  C.  Adams,  and  G.  D.  Liveing.     Only  small  parts  of 
the  collection  have  as  yet  been  published.] 

3  [The   correspondence   with    Cotes  and    some   other   letters    were 


NE  WTON  7 

At  his  mother's  second  marriage,  Newton  passed 
under  the  care  of  his  grandmother.  After  some 
education  at  day  schools,  he  was  placed,  in  his 
twelfth  year,  at  the  public  school  at  Grantham. 
He  distinguished  himself  here  by  a  turn  for 
mechanics  and  carpentering  ;  and  among  his  early 
tastes  was  the  love  of  writing  verses,1  and  of  draw- 
ing.2 The  dials  which  he  made  on  the  wall  of  his 
family  house  at  Woolsthorpe  have  lasted  to  our  day. 
They  were  lately  carefully  cut  out  by  Mr  Turner, 
and  presented,  framed  in  glass  for  preservation,  to 
the  Royal  Society.3  While  at  Grantham  he  formed 
a  friendship,  which  afterwards  became  a  more  serious 
feeling,  with  a  young  lady  named  Storey,  who  lived 
with  the  family  in  which  he  boarded.  Their 
marriage  was  prevented  by  their  poverty,  Miss 
Storey  was  afterwards  twice  married,  and  as  Mrs 
Vincent,  at  the  age  of  eighty-two,  after  Newton's 
death,  gave  many  particulars  concerning  his  early 
life.  He  continued  her  friend  to  the  end  of  his 
life,  and  was  her  frequent  benefactor  :  and  he  lived 

published  by  Edleston  in  the  above-mentioned  work.  On  other  manu- 
scripts of  Newton's,  see  W.  W.  Rouse  Ball,  op.  cit.,  pp.  2-5,  where 
"  Snirburn  Castle"  is,  as  in  G.  J.  Gray,  op.  cit.,  p.  75,  misspelt 
"  Sherborn  Castle" — a  mistake  that  may  give  rise  to  a  confusion  of 
two  different  places,  near  Wallingford  in  Berkshire  and  in  Dorset 
respectively.] 

1  [See  Brewster,  Memoirs,  1855,  vol.  i,  pp.  12-13.] 

2  [According   to   Newton's  own  later  confession,  he  was  extremely 
inattentive  to  his  studies  and  stood  very  low  in  the  school ;  but  soon, 
owing  to  the  excitation  of  a  spirit  of  emulation,  he  exerted  himself  in 
the  preparation  of  his  lessons  and  finally  rose  to  the  highest  place  in 
the  school  (Brewster,  Memoirs^  1855,  vol.  i,  pp.  7-8).     On  Newton's 
drawings,  see  ibid.,  p.  12.] 

:!  [But  cf.  Brewster,  Memoirs,  1855,  vo^  *>  PP«  11-12.] 


8  NE  WTON 

and  died  a  bachelor,  though  to  say  for  her  sake 
would  perhaps  be  going  beyond  evidence  ;  particu- 
larly when  the  engrossing  nature  of  his  subsequent 
studies  is  considered.1 


II 

When  he  was  fourteen  years  old  his  stepfather 
died,  and  his  mother,  who  then  took  up  her  residence 
at  Woolsthorpe,  recalled  him  from  school  to  assist 
in  the  management  of  the  farm.2  As  it  was  found, 
however,  that  he  was  constantly  occupied  with  his 
books  when  he  should  have  been  otherwise  engaged, 
his  maternal  uncle  recommended  that  he  should  be 
sent  to  Cambridge.  He  was  accordingly  admitted, 
on  June  the  5th,  1660,  a  member  of  Trinity  College, 
a  foundation  which  his  name  has  ever  since  not 
only  supported,  but  invigorated.  According  to  the 
college  books,  he  was  subsizar3  in  1661,  scholar  in 

1  [CJ.  Brewster,  Memoirs,  1855,  vol.  i,  pp.  13-14.] 

2  [On  Newton's  early  scientific  experiment  with  the  wind,  see  the 
third  Essay  below,  §  II.] 

a  A  sizar  at  Cambridge  was,  in  the  original  meaning  of  the  word, 
a  student  whose  poverty  compels  him  to  seek  to  maintain  himself  in 
whole  or  part  by  the  performance  of  some  duties  which  were  originally 
of  a  menial  character.  By  this  institution  a  youth  could  live  by  the 
work  of  his  hands  while  he  pursued  his  studies.  In  our  days  there 
is  but  little  distinction  between  the  sizars  and  those  above  them  ;  except 
in  college  charges,  none  at  all.  Those  who  look  upon  universities  as 
institutions  for  gentlemen  only,  that  is,  for  persons  who  can  pay  their 
way  according  to  a  certain  conventional  standard,  praise  the  liberality 
with  which  poorer  gentlemen  than  others  have  been  gradually  emanci- 
pated from  what  seems  to  them  a  mere  badge  of  poverty.  But  those 
who  know  the  old  constitution  of  the  universities  see  nothing  in  it 
except  the  loss  to  the  labouring  man  and  the  destitute  man  of  his 
inheritance  in  those  splendid  foundations.  If  sizarships  with  personal 


NE  WTON  9 

1664,  Bachelor  of  Arts  in  1665,  Junior  Fellow  in 
1667,  Master  of  Arts  and  Senior  Fellow  in  1668.  In 
1669,  Dr  Barrow  resigned  the  Lucasian  Professor- 
ship of  Mathematics,  and  Newton  was  appointed 
his  successor.  From  this  period,  when  all  money 
cares  were  removed  by  the  emoluments  of  his 
fellowship  and  professorship,  we  must  date  the 
beginning  of  Newton's  public  career. 

To  go  back  a  little  ;  it  does  not  appear  that 
Newton  went  to  Cambridge  with  any  remarkable 
amount  of  acquired  knowledge,  or  any  results  of 
severe  discipline  of  mind.  He  had  read  Euclid^  it 
is  said,  and  considered  the  propositions  as  self- 
evident  truths.1  This  is  some  absurd  version  of  his 

services  had  not  existed,  Newton  could  not  have  gone  to  Cambridge  ; 
and  the  Principia  might  never  have  been  written.  Let  it  be  re- 
membered, then,  that,  so  far  as  we  owe  this  immortal  work  and  its 
immortal  work  to  the  University  of  Cambridge,  we  owe  it  to  the 
institution  which  no  longer  exists,  by  which  education  and  advance- 
ment were  as  open  to  honest  poverty  seeking  a  maintenance  by  labour, 
as  to  wealth  and  rank.  Let  the  juries  who  find  on  their  oaths  that 
scores  of  pounds'  worth  of  cigars  are  reasonable  necessaries  for  young 
college  students,  think  of  this,  if  they  can  think.  [Cf.  Edleston, 
op.  cit.,  p.  xli.] 

1  [Before  Newton  left  Woolsthorpe,  his  uncle  had  given  him  a  copy 
of  Sanderson's  Logicy  which  he  seems  to  have  studied  so  thoroughly 
that,  when  he  afterwards  attended  lectures  on  that  work,  he  found 
that  he  knew  more  of  it  than  his  tutor.  Finding  him  so  far  advanced, 
his  tutor  told  him  that  he  was  about  to  read  Kepler's  Optics  to  some 
Gentlemen  Commoners,  and  that  he  might  attend  the  reading  if  he 
pleased.  Newton  immediately  studied  the  book  at  home,  and  when 
his  tutor  gave  him  notice  that  his  lectures  upon  it  were  to  begin,  he 
was  surprised  to  learn  that  it  had  been  already  mastered  by  his  pupil. 
About  the  same  time,  probably,  he  bought  a  book  on  Judicial  Astrology 
at  Stourbridge  fair — a  fair  held  yearly  in  Cambridge  in  September — and, 
in  the  course  of  perusing  it,  he  came  to  a  figure  of  the  heavens  which 
he  could  not  understand  without  a  previous  knowledge  of  trigonometry. 
He  therefore  bought  an  English  £uctid\vhh  an  index  of  all  the  problems 
at  the  end  of  it.  Having  turned  to  two  or  three  which  he  thought 
likely  to  remove  his  difficulties,  he  found  the  truths  which  they 


io  NEWTON 

early  studies  :  many  propositions,  no  doubt,  are  very 
evident ;  but  if  Newton  ever  gave  this  account  of 
himself,  which  we  do  not  believe,  it  proves  nothing 
but  that  the  lad  carried  to  the  University  as  much 
of  self-conceit  as  the  man  brought  away  of  learning 
and  judgment.  That  the  young  mechanician, 
desultory  in  the  previous  reading,  deep  beyond  his 
years  in  construction,1  and  practical  verification, 
found  within  himself  at  first  some  dislike  to  the 
beaten  road  of  mathematics,  and  was  willing  to 
make  it  royal  by  admitting  all  he  was  asked  to 
prove,  is  what  we  can  easily  believe  :  for  such  is  the 
most  frequent  tendency  of  an  unbalanced  exercise  of 
manual  ingenuity.  That  he  may  have  stated  this 
when  he  expressed  his  regret  that  he  had  not  paid 
greater  attention  to  the  geometry  of  the  ancients,  is 
not  improbable.  Were  such  his  bent,  the  discipline 
of  the  University  would  soon  show  a  mind  like  his 
the  paramount  necessity  of  a  different  mode  of  pro- 
enunciated  so  self-evident  that  he  expressed  his  astonishment  that  any 
person  should  have  taken  the  trouble  of  writing  a  demonstration  of 
them.  He  therefore  threw  aside  Euclid  "as  a  trifling  book,"  and 
set  himself  to  the  study  of  Descartes'  Geometry,  where  problems  not  so 
simple  seem  to  have  baffled  his  ingenuity.  Even  after  reading  a  few 
pages,  he  got  beyond  his  depth  and  laid  aside  the  work  ;  and  he  is  said 
to  have  resumed  it  again  and  again,  alternately  retreating  and  advancing, 
till  he  was  master  of  the  whole,  without  having  received  any  assistance. 
The  neglect  which  he  has  shown  of  the  elementary  truths  of  geometry 
he  afterwards  regarded  as  a  mistake  in  his  mathematical  studies,  and 
expressed  his  regret  that  "he  had  applied  himself  to  the  works  of 
Descartes  and  other  algebraic  writers  before  he  had  considered  the 
Elements  of  Euclid  with  that  attention  which  so  excellent  a  writer 
deserved  "  (Brewster,  Memoirs,  1855,  vol.  i,  pp.  21-22;  cf.  the  third 
Essay  below,  §  II.).] 

1  Let  it  be  remembered  that  we  are  not  told  that  Newton,  when  very 
young,  took  greatly  to  anything  except  arts  of  construction. 


NE  WTON  1 1 

ceeding.1  Again,  we  are  not  told  anything  of 
Newton's  pupillar  career  at  Cambridge,  except  that 
he  is  known  to  have 2  bought  a  prism  (an  epoch  in 
his  life)  in  1664  ;3  and  that,  in  the  same  or  the  next 
year,  being  competitor  for  a  college  law-fellowship 
with  a  Mr  Robert  Uvedale,  the  two  candidates  were 
of  perfectly  equal  merit,  and  Dr  Barrow  accordingly 
elected  Mr  Uvedale  as  the  senior  in  standing.  We 
have  no  account  of  any  great  sensation  produced  by 
the  talents  of  Newton  during  his  college  career. 


1  [See  §  II.  of  the  third  Essay  below  for  De  Morgan's  opinion  on  the 
story  of  Barrow  forming,  after  an  examination  of  Newton  in  Euclid  in 
1664,  an  indifferent  opinion  of  Newton's  knowledge  (Brewster,  Memoirs, 
vol.  i,  p.  24).] 

2  The  status  pupillaris  lasts  about   seven  years,  that  is,  until    the 
degree  of  Master  of  Arts  is  taken. 

3  [The  study  of  Descartes'  Geometry  seems  to  have  inspired  Newton 
with  a  love  of  the  subject,  and  to  have  introduced  him  to  higher  mathe- 
matics— the  study  of  the  works  of  Vieta,  Schooten,  and  Wallis.     In  a 
note-book  partly  written  in  1663-1664,  in  which  mathematical  notes  on 
these  writers  were  made,  he  also  wrote   down  some  observations  on 
refraction,  on  the   grinding  of  spherical  lenses,  and  on  the  errors   of 
lenses  and  the  method  of  rectifying  them.     An  entry  in  this  same  book 
made  by  Newton  in  1699  is  the  statement  that  the  annotations  out  of 
Schooten  and  Wallis  were  made  in  the  winter  between  1664  and  1665. 
At   this   time  he  found   the  Method    of  Infinite  Series ;  and,    in   the 
summer  of  1665,  being  forced  from  Cambridge  by  the  plague,  he  com- 
puted the  area  of  the  hyperbola  at  Boothby  in  Lincolnshire  to  fifty-two 
figures  by  the  same  method  (Brewster,  Memoirs,  1855,  vol.  i,  pp.  23-24; 
vol.  ii,  pp.  10-15).     In  1665  Newton  committed  to  writing  his  first  dis- 
covery of  the  method  of  fluxions.     This  paper  was  written  by  his  own 
hand,  and  dated  May  the  2Oth,  1665,  and  the  notation  of  dotted  letters  was 
here  used.     On  another  leaf  of  the  same  note-book,  the  method  was  de- 
scribed under  the  date  of  May  the  i6th,   1666.     In  the  same  book  again, 
with  a  date  of  November  the  I3th,  1665,  there  was  written  another  paper 
on  fluxions  with  their  application  to  the  drawing  of  tangents  and  "  the 
finding   of  the  radius   of  curvity  of  any   curve."     In   October    1666, 
Newton  drew  up  another  small  tract,  in  which  the  method  of  fluxions 
was  again  put  down  without  the  notation  of  dotted  letters  and  applied 
to  equations  involving  fractions  and  surds  and  such  quantities  as  were 
afterwards   called  transcendent  (ibid.     See  also  the  Appendix  to   the 
second  Essay  below).  ] 


12  NEWTON 

Even  Barrow,  the  best  judge  in  Cambridge,  and, 
after  Walk's,  in  England,  writing  to  Collins  in  1669 
(when  he  was  on  the  point  of  resigning  the  mathe- 
matical chair  to  Newton),  mentions  him  as  an  un- 
known man l  of  great  promise,  in  terms  of  high,  but 
not  unusual  commendation. 


ill 

The  first  period  of  Newton's  life  is  twenty-seven 
years,  ending  with  his  appointment  to  the  Lucasian 
professorship.  The  second,  of  twenty-six  years, 
ending  with  his  appointment  to  his  first  office  in 
the  Mint  in  i695,2  was  the  period  of  the  announce- 
ment of  all  his  discoveries.  The  third  and  longest, 
of  thirty-two  years,  containing  his  official  residence 
in  London,  saw  him  in  the  uninterrupted  possession 
of  as  much  fame  as  man  can  have,  and  power  never 
equalled  over  those  of  the  same  pursuits  as  himself. 
The  merely  biographical  history  of  his  second  period 
is  not  long.  On  Dec.  the  2ist,  1671,  and  Jan.  the 
nth,  1672,  the  Royal  Society  entered  on  their 

1  "A  friend  of  mine   here,    that  hath  an  excellent  genius  to  these 
things,    brought   me  .   .  .  papers  .  .  .  which   I   suppose   will    please 
you."     And    again,  some  days   after,  "  I  am   glad  my  friend's   paper 
gives  you  so  much  satisfaction  ;  his  name  is  Mr  Newton,  a  Fellow  of 
our   College,  and   very  young  (being  but  the  second  year  Master   of 
Arts),  but  of  an  extraordinary  genius  and  proficiency  in  these  things." 
[Barrow  sent  Newton's  tract  De  Analysis  Collins  on  July  the  3ist,  1669 
(Brewster,  Memoirs,  1855,  vol.  i,  pp.  27,  36;  vol.  ii,  pp.  14-15).] 

2  [Newton  was  appointed  Warden  of  the  Mint  in  1696,  and  Master  of 
the  Mint  in  1699.     Cf.  Edleston,  op.  «>.,  pp.  xxxv,  Ixviii ;  Brewster, 
Memoirs,  1855,  vol.  ii,  pp.  191-193-] 


NEWTON  13 

minutes,  in  such  terms  as  people  use  who  have  not 
the  gift  of  prophecy,  two  of  the  most  important 
announcements  they  ever  had  to  make.  f<  Mr  Isaac 
Newton,  Professor  of  Mathematics  in  the  University 
of  Cambridge,  was  proposed  candidate  by  the  Lord 
Bishop  of  Salisbury  (Dr  Seth  Ward),"  and  "Mr 
Isaac  Newton  was  elected."  During  the  whole  of 
this  second  period,  he  was  seldom  out  of  Cambridge 
more  than  three  or  four  weeks  in  one  year.  Having 
missed  the  Law  Fellowship  (which  was  a  lay  fellow- 
ship), he  would  have  been  required,  in  1675,  either 
to  take  orders  or  to  vacate  the  fellowship  which  he 
did  hold.  But  in  that  year  he  obtained  a  dispensa- 
tion from  Charles  II.,  no  doubt  granted  at  the  appli- 
cation of  the  College.  He  lectured  on  optics  in  the 
year  following  his  appointment  to  the  professorship  ; 
and  it  would  appear  that  he  lectured  on  elementary 
mathematics.  ^\\Q  Arithmetica  Universalis  (published 
by  Whiston,  it  was  said,  against  Newton's  consent, 
which  Whiston  denies)  was  taken  from  the  lectures 
delivered  on  algebra  and  its  application  to  geometry, 
which  were  preserved  in  the  depositories  of  the  Uni- 
versity.1 When,  in  1687,  James  II.,  among  his 
other  attempts  of  the  same  kind,  ordered  the  Uni- 
versity of  Cambridge  to  admit  a  Benedictine  as 
Master  of  Arts  without  taking  the  oaths,  and  upon 

1  [Newton's  lectures  on  optics,  arithmetic,  and  algebra,  on  the  motion 
of  bodies,  and  on  the  system  of  the  world,  are  preserved  in  the  University 
Library  at  Cambridge,  and  are  described  in  Edleston  ;  op.  cit.,  pp. 
xci-xcviii.  Cf.  also  W.  W.  Rouse  Ball,  op.  cit.,  pp.  27-28.] 


14  NEWTON 

the  resistance  of  the  University,  Newton  was  appointed 
one  of  the  delegates  to  the  High  Court  for  the  purpose 
of  stating  the  case.  The  king  withdrew  his  order, 
and  in  the  next  year  Newton  was  proposed  as 
Member  of  Parliament  for  the  University,  and  gained 
his  election  by  a  small  majority.  He  sat  accordingly 
in  the  Convention  Parliament,  which  declared  the 
throne  vacant,  though  it  appears  by  the  records  of 
the  College  that,  except  in  1688  and  1689,  he  was 
not  absent  from  the  University  often  enough  or 
long  enough  to  have  taken  much  share  in  public 
business. 

IV 

In  1692  occurred  the  curious  episode  of  his  history 
which  produced  abroad,  as  has  recently  appeared,  a 
report  that  he  had  become  insane.  Most  readers 
know  the  tradition  of  his  dog  Diamond  having  up- 
set a  light  among  the  papers  which  contained  his 
researches,  and  of  the  calmness  with  which  he  is 
said  to  have  borne  the  loss.  The  truth,  as  appears 
by  a  private  diary  of  his  acquaintance  Mr  de  la 
Pryme,  recently  discovered  is,  that  in  February  1692, 
he  left  a  light  burning  when  he  went  to  chapel,  which, 
by  unknown  means,  destroyed  his  papers,  and  among 
them  a  large  work  on  optics,  containing  the  experi- 
ments and  researches  of  twenty  years.  "  When  Mr 
Newton  came  from  chapel,  and  had  seen  what  was 
done,  everybody  thought  that  he  would  have  run 


NEWTON  15 

mad  ;  he  was  so  troubled  thereat  that  he  was  not 
himself  for  a  month  after."  Such  phrases,  reported, 
gave  rise  to  a  memorandum  in  the  diary  of  the 
celebrated  Huygens  (the  first  foreigner  who  under- 
stood and  accepted  the  theory  of  gravitation),1 
stating  that  he  had  been  told  that  Newton  had 
become  insane,  either  from  study,  or  from  the  loss 
of  his  laboratory  and  manuscripts  by  fire — that 
remedies  had  been  applied  by  means  of  which  he 
had  so  far  recovered  as  to  be  then  beginning  again 
to  understand  his  own  Principia.  That  Newton 
was  in  ill-health  in  1692  and  1693  is  known,  but  his 
letters  to  Dr  Bentley  on  the  Deity,  written  during 
that  period,  are  proof  that  he  had  not  lost  his 
mind.2 

We  now  give  a  slight  enumeration  of  the  matters 
on  which  Newton's  attention  was  fixed  during  the 
second  period,  which  we  have  just  quitted.3 

1  [This  is  hardly  correct;  cf.   Rosenberger,  op.  cit.t  p.  234,  and  the 
whole  of  that  chapter.] 

2  [See   Brewster,  Memoirs,  vol.  ii,  pp.    123-124,   131-156;   on   the 
letters  to  Bentley,  cf.  Rosenberger,  op.  ctt.,  pp.  263-270.] 

3  [The  only  complete  edition  of  Newton's  works  was  edited  by  Bishop 
S.    Horsley  in   five   volumes  from    1779-1785   under  the  title   Isaaci 
Newtoni  Opera  qua  existant  omnia.      Conimentariis  illustrabat  Samuel 
Horsley.     Contents:    Vol.  i,  (i)  Arithmetica  Universalis.    (2)  Tractatus 
de  Raiionibus  Primis  Ultimisque.     (3)  Analysis  per  yEquationes  numero 
terminorum   Infinitas.     (4)   Excerpta  quaedam   ex   Epistolis  ad   Series 
Fluxionesque    pertinentia.     (5)    Tractatus   de    Quadratura   Curvarum. 
(6)  Geometria  Analytica  sive  specimina  Artis  Analyticae.     (7)  Methodus 
Differentialis.      (8)    Enumeratio    Linearum    tertii    Ordinis.      Vol.    ii, 
Principiorum   Libri   Priores  duo,  De    Motu  Corporum.      Vol.  iii,  (i) 
Principiorum    Liber   Tertius,    de   Systemate   Mundi.     (2)    De   Mundi 
Systemate.      (3)  Theoria    Lunse.     1(4)   Lectiones   Opticae.      Vol.    iv, 
(i)  Opticks.     (2)  Letters  on  various  Subjects  in   Natural  Philosophy, 
published   from  the    Originals  in  the  Archives  of  the  Royal  Society. 
(3)  Letters  to  Mr  Boyle  on  the  Cause  of  Gravitation.     (4)  Tabulae  Duae, 


1 6  NEWTON 

V 

OPTICS 

The  great  discovery  of  the  unequal  refrangibility 
of  the  rays  of  light  was  made  in  1666,  the  year  in 
which  he  was  driven  from  Cambridge  by  the  plague. 
In  1668  he  resumed  his  inquiries,  and,  judging  that 
the  decomposition  of  light  which  he  had  discovered 
would  render  it  impossible  to  construct  refracting 
telescopes  free  from  colour,  or  achromatic,  he  applied 
himself  to  the  improvement  of  the  reflecting  tele- 
scope. The  telescope  which  he  made  with  his  own 
hands,  now  in  possession  of  the  Royal  Society,  was 
made  in  1671.  It  was  submitted  to  the  Society 

Color um  altera,  altera  Refractionum.  (5)  De  Problematibus  Bernoul- 
lianis.  (6)  Propositions  for  determining  the  Motion  of  a  Body  urged 
by  two  Central  Forces.  (7)  Four  Letters  to  Dr  Bentley.  (8)  Com- 
mercium  Epistolicum,  etc.,  cum  recensione  prsemissa.  (9)  Additamenta 
Commercii  Epistolici  ex  Historia  Fluxionum  Raphsoni.  Vol.  v,  (i) 
Chronology  of  Antient  Kingdoms  amended.  (2)  Short  Chronicle  from 
a  MS.  the  property  of  the  Rev.  Dr  Ekins.  (3)  Observations  upon  the 
Prophecies  of  Holy  Writ,  particularly  the  prophecies  of  Daniel  and  the 
Apocalypse  of  St  John.  (4)  An  Historical  Account  of  two  Notable 
Corruptions  of  Scripture,  in  a  Letter  to  a  Friend.  Horsley  added  the 
following  papers  :  (i)  Logistica  Infinitorum,  (2)'Geometria  Fluxionum 
sive  Additamentum  tractatus  Newtoniani  de  Rationibus  Primis  Ultimis- 
que,  in  vol.  i ;  (3)  De  viribus  centralibus  quae  rationem  triplicate  dis- 
tantiarum  a  centro  contrariam  inter  se  constanter  servant,  in  vol.  iii. 
A  Latin  edition  of  Newton's  works  was  published  at  Lausanne  and 
Geneva  in  1744,  and  is  described  in  G.  J.  Gray,  op.  cit.t  pp.  2-4.  The 
various  editions,  from  1687  on,  of  the  Prindpia,  and  its  translations 
and  commentaries  were  described  by  Gray  (ibid.,  pp.  5-35).  Here  we 
will  only  mention  that  the  only  complete  English  translation  of  it  was 
by  Andrew  Motte,  and  was  first  published  at  London  in  1729  (American 
editions,  New  York,  1848  and  1850),  and  that  the  selection  of  works 
mentioned  in  Gray's  ' '  Illustrations "  is  often  ludicrous.  Gray  dealt 
with  books  on  optics,  fluxions,  universal  arithmetic,  and  minor  works 
by  Newton  and  others  on  pp.  35-46,  46-55,  56-59,  and  59-61 
respectively.] 


NEWTON  17 

immediately  after  his  election  as  a  Fellow,  and  was 
followed  by  the  account  of  his  discovery  of  the 
decomposition  of  light.  This  explanation  of  the 
known  phenomenon  of  the  colours  of  the  prismatic 
spectrum  was  fully  appreciated  by  the  Society  ;  but 
Newton  had  to  reply  to  various  objections  from 
foreign  philosophers,  and  to  those  of  Hooke  at  home. 
At  this  time  first  appeared  (indeed  there  had  been 
nothing  before  to  draw  it  out)  that  remarkable  trait 
in  his  character  of  which  we  shall  afterwards  speak  : 
extreme  aversion  to  all  kinds  of  opposition.  ' 1 1 
intend,"  he  says,  "to  be  no  further  solicitous  about 
matters  of  philosophy."  And  again,  "I  was  so 
persecuted  with  discussions  arising  from  the  publi- 
cation of  my  theory  of  light,  that  I  blamed  my  own 
imprudence  for  parting  with  so  substantial  a  blessing 
as  my  quiet  to  run  after  a  shadow." 

The  researches  on  the  colours  of  thin  plates,  and 
the  explanation  known  by  the  name  of  the  theory 
of  "  Fits  of  Reflexion  and  Transmission,"  was  com- 
municated to  the  Royal  Society  in  1765-66.  Those 
on  the  ''inflexion"  of  light,  though  probably  made 
long  before  1704,  first  appeared  in  that  year,  in  his 
treatise  on  Opticks.  He  never  would  publish  this 
work  as  long  as  Hooke  lived,  from  that  fear  of 
opposition  above  noted.1 

1  [On  Newton's  optical  researches,  see  Brewster,  Memoirs •,  1855, 
vol.  i,  pp.  37-249  ;  Rosenberger,  op.  «'/.,  pp.  51-117,  289-341.] 


1 8  NEWTON 

VI 

PRINCIPIA  :   THEORY   OF   UNIVERSAL   GRAVITATION 

The  discoveries  of  Kepler1  had  laid  down  the 
actual  laws  of  the  planetary  motions  :  and  the  idea 
of  universal  gravitation  began  to  occupy  the  minds 
of  those  who  thought  on  these  subjects.  "  Gravita- 
tion "  was  a  term  of  some  antiquity,  used  to  denote 
the  effort  of  bodies  on  the  earth  to  descend  :  weight L, 
in  fact.  The  notion  of  matter  acting  upon  matter 
as  an  agent  of  attracting  force,  and  the  possibility 
of  such  force  extending  through  the  heavens,  and 
being  the  proximate  cause  of  the  motions  of  the 
planets,  was  floating  through  men's  minds  when 
Newton  first  turned  his  attention  to  the  subject. 
There  has  hardly  ever  been  a  great  discovery  in 
science,  without  its  having  happened  that  the  germs 
of  it  have  been  found  in  the  writings  of  several 
contemporaries  or  predecessors  of  the  man  who 
actually  made  it.  In  the  case  before  us  it  had  even 
been  asserted  as  matter  of  necessity,  that  supposing 
attraction  to  exist,  it  must  be  according  to  the  law 
of  the  inverse  squares  of  the  distances : 2  and  Huygens 

1  [Kepler  (1571-1630)  discovered  in  1609,  from  the  observations  of 
Tycho  Brahe  and  himself,  that  the  planets  move  round   the   sun   in 
ellipses  in  one  of  whose  foci  the  sun  is  placed,  and  that  the  line  join- 
ing  sun   and   planet   describes   equal   areas  in  equal  times.     In  1619 
he  published  his  further  discovery  that  the  periodic  times  of  any  two 
planets  are  to  one  another  as  the  cubes  of  their  distances  from  the  sun.] 

2  [On   the   precursors   of  Newton,  and   especially  Kepler,  Galileo, 
Descartes,    Bouillaud,    Borelli,    and   Hooke,   see   Brewster,  Memoirs, 
1855,  vol.  i,  pp.  250-288:  Rosenberger,  op.  cit.>  pp.  135-157.] 


NEWTON  19 

announced,  in  1673,  before  Newton  had  completed 
any  part  of  his  system,  the  relations  which  exist 
between  attractive  force  and  velocity  in  circular 
motion.1  Newton  first  turned  his  attention  to  the 
subject  in  1666,  at  Woolsthorpe  ;  sitting  alone  in  a 
garden,  his  thoughts  turned  towards  that  power  of 
gravity  which  extends  to  the  tops  of  the  highest 
mountains,  and  the  question  whether  the  power 
which  retains  the  moon  in  her  orbit  might  not  be 
the  same  force  as  that  which  gives  its  curvature  to 
the  flight  of  a  stone  on  the  earth.  To  deduce  from 
what  Kepler  had  exhibited  of  the  laws  of  the 
planetary  motions,  that  the  force  must  vary  in- 
versely as  the  square  of  the  distance,  came  within 
his  power  :  but  on  trying  the  value  of  that  force,  as 
deduced  from  the  moon's  actual  motion,  with  what 
it  should  be  as  deduced  from  the  force  of  gravitation 
on  the  earth,  so  great  a  difference  was  found  as  to 
make  him  throw  the  subject  aside.  The  reason  of 
his  failure  was  the  inaccurate  measure  which  he  used 
of  the  size  of  the  earth.2  The  subject  was  not 

1  [This  was  in  his  Horologium  Osdllatorium   of  1673   (see    Mach, 
op.  ctt.,  pp.  155-187).     At  the  end  of  the  book  were  given  some  rules 
for  the   calculation  of  centrifugal  forces   in  circular  motions ;  but  no 
demonstrations  were  there  given,  and  these  demonstrations  were  only 
supplied  by  him  in  a  tract  published  posthumously,  in  1703,  and  trans- 
lated into  German  in  No.   138  of   OstwalcTs  Klassiker.     It   must   be 
remembered  that  Newton  had  used  the  chief  result  of  Huygens  in  this 
direction  in  his  earliest  and  unpublished  investigation  on  gravity  and 
the  moon's  orbit,  in  1666.] 

2  [It  is  now  usually  maintained,  on  certain   grounds   that  are   dis- 
cussed in  W.   W.   Rouse  Ball,  op.  cit.,  pp.  7,  II,  16-17,  61,  157,  that 
Newton  was  fairly  well  satisfied  with  the  result   of  his   approximate 
calculation  of  1666,  and  had  a  strong  suspicion  of  the  law  of  universal 


20  NE  WTON 

resumed  till  1679;  not,  as  commonly  stated,  be- 
cause he  then  first  became  acquainted  with  Picard's 
measure  of  the  earth  (we  think  Professor  Rigaud 
had  shown  this),  but  because  leisure  then  served, 
and  some  discussions  on  a  kindred  subject  at  the 
Royal  Society  had  awakened  his  attention  to  the 
question.1  In  1679  he  repeated  the  trial  with 
Picard's  measure  of  the  earth  :  and  it  is  said  that 
when  he  saw  that  the  desired  agreement  was  likely 
to  appear,  he  became  so  nervous  that  he  could  not 
continue  the  calculation,  but  was  obliged  to  intrust 
to  a  friend.2  From  that  moment  the  great  dis- 
covery must  be  dated  :  the  connexion  of  his  specu- 
lations on  motion  with  the  actual  phenomena  of  the 
universe  was  established.  At  the  time  when  we 
write  this,  a  distant  result  of  that  calculation  has 
been  announced,  which  Newton  himself  would  hardly 

at  any  period  of  his  life  have  imagined  to  have  been 

/ 

gravitation,  but  he  was  stopped  by  the  difficulty  of  calculating  the 
attractions  of  a  number  of  particles  massed  together.  This  he  dis- 
covered— at  least  in  the  most  important  case — in  1685,  and  thus  the 
propositions  which  he  had  previously  (1679  an{^  1680)  found  about  the 
orbits  of  attracting  particles  could  be  applied  at  once  to  spherical  bodies. 
Newton,  in  fact,  discovered  in  1685  by  calculation  that  such  bodies 
attract  as  if  they  were  particles  situated  at  the  contents  of  the  masses. 
Thus  he  must  have  only  then  realised  that  those  propositions,  which  he 
had  believed  to  be  only  approximately  true  when  applied  to  the  solar 
system,  were  almost  completely  exact.] 

1  [The  subject  was  certainly  resumed  in  1679,  but  it  was  apparently 
in  consequence  of  a  problem  proposed  by  Robert  Hooke  in  a  letter  to 
Newton  of  N  ovember  of  that  year.     In  the  correspondence  that  followed, 
Hcoke   drew    attention    to    Picard's    measurements,    and    stimulated 
Newton's   interest   and   curiosity  by   his   happy   insight   into   celestial 
problems  and  correction  of  a  careless  remark  of  Newton's.     For  this 
correspondence,  see  W.  W.  Rouse  Ball,  op.  cit.,  pp.  18-24,  139-153.] 

2  [This   story  is  probably  apocryphal ;  cf.  W.  W.   Rouse  Ball,  op. 
cit.,  p.  23.] 


NEWTON  21 

possible.  A  planetary  body,  unknown  and  unseen 
till  after  the  prediction,  has  made  itself  felt  by 
its  attraction  on  another.  Unexplained  (and  very 
trivial)  irregularities  in  the  motion  of  Uranus  sug- 
gested the  idea  of  there  being  yet  another  planet 
by  the  attraction  of  which  they  were  produced. 
From  those  irregularities  the  place  and  distance  of 
that  planet  have  been  inferred,  and,  on  looking  into 
the  part  of  the  heavens  at  which  its  silent  action 
proved  it  to  be,  if  indeed  it  existed — there  it  was 
found.  A  heavenly  body  has  thus  been  calculated 
into  existence,  as  far  as  man  is  concerned.1 

How  much  Newton  might  have  got  ready  it  is 
not  easy  to  say  :  all  that  is  known  is  that  he  kept 
it  to  himself.  At  the  end  of  1683  Halley 2  had 
been  considering  the  question,  and  was  stopped  by 
its  difficulties ;  but,  being  in  August  1684  on  a 
visit  to  Newton,  the  latter  informed  him  of  what 
he  had  done,  but  was  not  able  to  find  his  papers. 
After  Halley's  departure,  he  wrote  them  again,  and 
sent  them  :  upon  which  Halley  paid  another  visit 
to  Cambridge,  to  urge  upon  Newton  the  continuance 

1  [The  almost  simultaneous  discovery  in  1846  of  Uranus  by  Adams 
and  Le  Verrier,  by  calculation,  created  a  most  powerful  impression  on 
nearly  everybody,  including  De  Morgan  (cf.  Mrs  De  Morgan's  Memoir, 
pp.  126-138).] 

2  [The   biographical   sketch  of  Halley   (1656-1742)  in  the  Cabinet 
Portrait  Gallery  of  British  Worthies,  vol.  xii,  London,  1847,  pp.  5-15, 
is,  judging  from  the  style,  by  De  Morgan.     From  Mrs  De  Morgan's 
Memoir,  p.   108  (see  the  first  note  to  the  first  Appendix  to  the  third 
Essay  below),  we  learn  that  De  Morgan  wrote  the  article  "Halley" 
on  pp.  161-168  of  the  first  volume  of  The  Gallery  of  Portraits :  with 
Memoirs  (London,   1833).      The  biography  of  Newton  on  pp.  79-88 
of  this  volume  does  not  seem  to  be  by  De  Morgan.] 


22  NE  WTON 

of  his  researches  ;  and  (December,  1684)  informed 
the  Royal  Society  of  them,  and  of  Newton's  promise 
to  communicate  them.  The  Society,  who  knew 
their  man,  and  how  little  they  should  get  without 
asking,  appointed  a  Committee  (Halley  and  Paget, 
the  mathematical  master  in  Christ's  Hospital)  to 
keep  Newton  in  mind  of  his  promise ;  so  that 
(February,  1685)  a  communication  was  sent  up, 
amounting  to  those  parts  of  the  first  book  of  the 
Principia  which  relate  to  central  forces.  Newton 
went  on  with  the  work,  and  (April  the  2ist,  1686) 
Halley  announced  to  the  Society  that  "  Mr  Newton 
had  an  incomparable  treatise  on  Motion,  almost 
ready  for  the  press."  On  the  28th,  Dr  Vincent 
(the  husband,  it  is  supposed,  of  Miss  Storey)  pre- 
sented the  manuscript  of  the  first  book  to  the 
Society,  who  ordered  it  to  be  printed,  and  Halley 
undertook  to  pay  the  expenses.  But  it  was  not 
yet  in  harbour  :  Hooke,  who  used  to  claim  every- 
thing, asserted  that  he  had  been  in  possession  of 
the  whole  theory  before  Newton  ;  with  which  the 
latter  was  so  disgusted,  that  he  proposed  to  omit 
the  third  book  (being  in  fact  all  the  application  to 
our  system).  Halley,  the  guardian  angel  of  the 
work,  wrote  him  a  letter,  in  which  he  soothed  him 
almost  as  if  he  had  been  a  child,  and  prevailed  upon 
him  to  complete  it  as  first  intended.  It  appeared 
under  the  title  of  Philosophic  Naturalis  Principia 
Matheniatica^  about  midsummer,  1687,  containing 


NEWTON  23 

the  mathematical  discussion  of  the  laws  of  solid  and 
fluid  motion,  with  their  application  to  the  heavenly 
motions,  the  tides,  the  precession  of  the  equinoxes, 
and  so  on.  The  reader  who  understands  the  terms 
may  refer  to  the  Penny  Cyclopaedia  (article  *  *  Prin- 
cipia "),  in  which  the  heads  of  all  the  propositions 
are  given.  No  work  on  any  branch  of  human  know- 
ledge was  ever  destined  to  effect  so  great  a  change, 
or  to  originate  such  important  consequences.1 


VII 


FLUXIONS,    NOW   CALLED   THE   DIFFERENTIAL 
CALCULUS 

A  curved  figure  differs  from  one  the  boundaries  of 
which  are  consecutive  straight  lines  in  that  there  is 
always  a  gradual  change  of  direction  going  on  at 
the  boundaries  of  the  former,  while  at  those  of  the 
latter  the  changes  are  made  only  at  certain  places, 
and  as  it  were  in  the  lump.  To  apply  the  doctrines 
of  mathematics  to  cases  in  which  such  perfectly 
gradual  changes  take  place,  had  been  always  the 
greatest  difficulty  of  the  science.  Archimedes  had 
conquered  it  in  a  few  cases  :  the  predecessors  of 
Newton  had  greatly  extended  what  Archimedes 
had  done,  and  had  given  what,  to  those  who  come 

1  [On  Newton's  investigations  of  1684,  on  the  preparation  and  publi- 
cation of  the  Principia  (1685-1687),  for  Hal  ley's  correspondence  with 
Newton  (1686-1687)  about  the  publication  of  the  Principia  and  about 
Ilooke's  claims,  cf.  W.  W.  Rouse  Ball,  op.  cit.,  pp.  25-73,  153-174.] 


24  NE  WTON 

after  Newton  and  Leibniz,  would  appear  strong 
hints  of  an  organized  method  of  treating  all  cases. 
But  the  method  itself,  and  an  appropriate  language 
for  expressing  its  forms  of  operation,  were  still 
wanting.  About  1663,  Newton  turned  his  attention 
to  the  writings  of  Descartes  and  Wallis,  and,  in 
the  path  which  the  latter  had  gone  over,  found  the 
celebrated  Binomial  Theorem  :  Wallis  having  in 
fact  solved  what  would  now  be  called  a  harder 
problem.  This,  far  from  lessening  the  merit  of  the 
discovery,  increases  it  materially.  In  1665  Newton 
arrived  at  his  discoveries  in  series,  and  substantially 
at  his  method  of  fluxions.  In  1669  Barrow  com- 
municated to  Collins  (on  the  occasion  before  referred 
to)  a  paper  by  Newton  on  series,  not  containing 
anything  on  fluxions.  Various  letters  of  Newton, 
Collins,  and  others,  state  that  such  a  method  had 
been  discovered,  without  giving  it.  But  one  letter 
from  Newton  to  Collins  on  December  the  loth, 
1672,  states  a  mode  of  using  one  case  of  this  method, 
confined  to  equations  of  what  are  called  rational 
terms  (it  being  admitted  on  all  sides  that  the  great 
pinch  of  the  question  then  lay  in  equations  of 
irrational  terms].  Leibniz,  who  had  been  in 
England  in  1673,  and  had  heard  something  indefinite 
of  what  Newton  had  done,  desired  to  know  more  : 
and  Newton,  on  June  the  I3th,  1676,  wrote  a  letter 
to  Oldenburg,  of  the  Royal  Society,  which  he 
desired  might  be  communicated  to  Leibniz.  This 


NEWTON  25 

letter  dwells  on  the  binomial  theorem,  and  various 
consequences  of  it  ;  but  has  nothing  upon  fluxions. 
Leibniz  still  desiring  further  information,  Newton 
again  wrote  to  Oldenburg,  on  October  the  24th, 
1676,  explaining  how  he  arrived  at  the  binomial 
theorem,  giving  various  other  results,  but  nothing 
about  fluxions  except  in  what  is  called  a  cipher.  A 
cipher  it  was  not,  for  it  merely  consisted  in  giving 
all  the  letters  of  a  certain  sentence,  to  be  put  to- 
gether if  Leibniz  could  do  it.  Thus,  the  informa- 
tion communicated  was 

aaaaaa  cc  d  ae  eeeeeeeeeeeee  ff  iiiiiii  111  nnnnnnnnn 
oooo  qqqq  rr  ssss  ttttttttt  vvvvvvvvvvvv  x. 

These  are  merely  the  letters  of  a  Latin  sentence 
which,  translated  word  by  word  in  the  order  of  the 
words,  is  "  given  equation  any  whatsoever,  flowing 
quantities  involving,  fluxions  to  find,  and  vice  versa. "  1 
Even  this  letter  had  not  been  sent  to  Leibniz  on 
March  the  5th,  1677  ;  it  was  sent  soon  after  this  date. 
But  in  the  mean  time,  Leibniz,  by  himself,  or  as 
was  afterwards  said,  having  taken  a  hint  from  other 
letters  of  Newton,  had  invented  his  differential 
calculus.  And,  as  open  as  Newton  was  secret, 
shortly  after  receipt  of  the  above,  he  wrote  to 
Oldenburg,  on  June  the  2ist,  1677,  a  letter  giving  a 

1  [The  Latin  sentence  is :  "  Data  sequatione  quotcunque  fluentes 
quantitates  involvente,  fluxiones  invenire  ;  et  vice  versa."  The  anagram 
may  be  more  shortly  written : 

6a  2c  d  ae  136  2f  J\  3!  <)r\  40  4q  2r  45  Qt  I2v  x.] 


26  NE  WTON 

full  and  clear  statement  of  everything  he  had  arrived 
at  :  making  an  epoch  as  important  in  the  pure  mathe- 
matics, as  was  the  discovery  of  the  moon's  gravita- 
tion in  the  physical  sciences.  In  the  Principia, 
Newton  acknowledges  this  in  the  following 
"Scholium":  "In  letters  which  went  between 
me  and  that  most  excellent  geometer  G.  G.  Leibniz,1 
ten  years  ago,  when  I  signified  that  I  was  in  the 
knowledge  of  a  method  of  determining  maxima  and 
minima,  of  drawing  tangents  and  the  like,  and  when 
I  concealed  it  in  transferred  letters  involving  this 
sentence  ('  Data  aequatione,'  and  so  on,  as  above), 
that  most  distinguished  man  wrote  back  that  he  had 
also  fallen  upon  a  method  of  the  same  kind,  and 
communicated  his  method,  which  hardly  differed 
from  mine  except  in  the  forms  of  words  and  symbols. 
The  foundation  of  both  is  contained  in  this  Lemma." 
In  1684  Leibniz  published  his  method  :  while  in  the 
Principiay  Newton  still  gave  nothing  more  than  the 
most  general  description  of  it,  and  avoided  its  direct 
use  entirely.  By  1695  it  had  grown  into  a  power- 
ful system,  in  the  hands  of  Leibniz  and  the  Ber- 
noullis  :  while  in  England  it  was  very  little  noticed. 
About  1695  an  alarm  began  to  be  taken  in  England 
at  its  progress  :  and  the  friends  of  Newton  began  to 
claim  what  they  conceived  to  be  his  rights.  Wallis 
excused  himself  from  mentioning  the  differential 

1  [Leibniz's  names  were   Gottfried  Wilhelm  ;   the  initials  "  G.  G." 
(Gothofredus  Gulielmus)  stand  for  the  Latin  version  of  these  names.] 


NEWTON  27 

calculus  in  his  works,  on  the  ground  that  it  was 
Newton's  method  of  fluxions.  In  1699,  Fatio  de 
Duillier,  a  Genevese  residing  in  England,  published 
an  implied  charge  of  plagiarism  on  Leibniz :  the 
latter  denied  the  imputation  and  appealed  to  Newton's 
own  testimony.  The  Leipsic  Acts *  made  something 
very  like  the  same  charge  against  Newton  :  and  in 
the  course  of  the  dispute,  Keill,  an  Englishman, 
asserted  2  that  Leibniz  had  taken  Newton's  method, 
changing  its  name  and  symbols.  This  accusation 
roused  Leibniz,  who  complained  to  the  Society  :  and 
after  some  correspondence,  in  which  allusion  was 
made  to  the  Oldenburg  letters  as  being  sources 
from  which  he  might  have  drawn  knowledge  of 
Newton's  method,  the  Royal  Society  appointed  a 
Committee,  consisting  of  eleven  members,  to  examine 
the  archives,  and  to  defend  Newton.  This  latter 
purpose,  though  not  stated  in  words,  was  fully 
understood  :  and  since  the  usual  impression  is  that 
it  was  intended  for  a  judicial  committee,  meaning 
of  course  an  impartial  one,  we  give  in  a  note3  some 

1  [The  remark  referred  to  was  in  an  anonymous  review  by  Leibniz, 
but  was  by  no  means  a  charge  of  plagiarism.     (Cf.  Rosenberger,  op. 
cit.,  pp.  473-475)-] 

2  Phil.  Trans.,  1708. 

3  First,  the  Committee  consisted  of  Halley,  Jones,  De  Moivre,  and 
Machin,    Newton's    friends,    and    mathematicians ;    Brook    Taylor,    a 
mathematician,  but   not   then  otherwise   known  except  as  a  friend  of 
Keill,  the  accused  party  ;  Robarts,  Hill,  Burnet,  Aston,  and  Arbuthnot, 
not   known  as  mathematicians,  but   the   two   latter  intimate   personal 
friends  of  Newton  ;   and  Bonet,  the   Prussian  minister.     To  call  this 
a  judicial  committee  would  be  to  throw  a  great  slur  on  the  Society. 
Secondly,  the  names  of  the  Committee  were  never  published  with  their 
report,  which  would  have  been  anything  but  creditable,  if  that  report 


28  NE  WTON 

heads  of  the  proof  of  our  assertion.  The  Committee, 
appointed  at  different  times  in  March  1712,  reported 
in  April  that  they  had  examined,  and  so  on,  and 
that  they  were  of  opinion  that  Leibniz  had  no 
method  till  after  the  letter  to  Collins  of  December  the 
loth,  1672,  had  been  sent  to  Paris  to  be  communi- 
cated to  him,  and  that  Keill,  in  asserting  the  priority 
of  Newton,  had  done  Leibniz  no  injustice.  This 
is,  to  us,  the  main  part  of  the  report.  It  was 
published,  with  abundance  of  extracts  from  letters, 
and  letters  at  length,  most  of  which  had  been  found 
among  Collins's  papers,  under  the  name  of  Com- 
mercium  Epistolicum,  and  so  on,  in  1712  and  in 
1725.  The  conclusion  was  not  to  the  point  : 
Leibniz  asked  reparation  for  a  charge  of  theft,  and 
the  answer  is  that  there  was  no  injustice  to  him  in 
saying  that  the  other  party  had  the  goods  before 
the  time  when  he  was  alleged  to  have  stolen  them. 

had  been  a  judgment :  but  if  the  Committee  were  only  counsel  for 
Newton's  case  it  mattered  not  who  they  were.  Thirdly,  the  Society 
had  committed  .itself  to  Newton's  side,  by  hearing  his  statement,  and 
thereupon  directing  Keill  to  write  the  second  letter  in  the  controversy, 
and  to  "set  the  matter  in  a  just  light "  :  the  only  light  they  had  sought 
being  that  which  Newton  himself  could  give.  Fourthly,  Burnet  wrote 
to  John  Bernoulli  while  the  matter  was  pending,  stating  in  express  terms 
— not  that  the  Royal  Society  was  inquiring — but  that  it  was  busy  proving 
that  Leibniz  might  have  seen  Newton's  letters.  Fifthly,  De  Moivre,  as 
appears  by  the  statement  of  an  intimate  friend,  considered  himself,  by 
merely  joining  that  Committee,  as  drawn  out  of  the  neutrality  which  he 
had  till  then  observed  :  which  shows  that  he  did  not  consider  himself  a 
juryman.  Sixthly,  no  notice  was  given  to  Leibniz  of  the  proceeding, 
still  less  an  invitation  to  produce  documents  on  his  own  side.  All  these 
things  put  together  show  that  the  Committee  was  not  judicial,  nor  meant 
to  be  so,  nor  asserted  to  be  so  on  the  part  of  the  Society.  If  any  one 
will  have  it  that  it  was  so,  he  must  needs,  we  think,  hold  that  it  was 
one  of  the  most  unfair  transactions  which  ever  took  place. 


NE  WTON  29 

With  regard  to  Collins's  letter,  besides  its  contain- 
ing no  more  than  any  good  mathematician  could 
have  drawn  from  Barrow  and  Fermat  together,  no 
proof1  was  given  to  the  world  of  Leibniz  ever  having 
seen  it,  which  any  man  who  valued  his  character 
would  have  ventured  to  produce  in  any  kind  of  court 
with  rules  of  evidence.  In  truth,  though  the  Com- 
mittee were  not  unfair  judges  (simply  because  they 
were  not  judges  at  all),  we  cannot  but  pronounce 
them  unscrupulous  partisans,  for  the  reasons  given 


1  A  parcel  (collectio)  of  extracts  from  Gregory's  letters  are  found  in 
the  handwriting  of  Collins,  with  a  memorandum  by  Collins  that  they 
were  to  be  sent  to  Leibniz  and  returned  by  him  :  with  a  letter  to 
Oldenburg,  desiring  him  to  send  them :  no  mention  of  any  one  but 
Gregory  in  either  memorandum  or  letter.  With  the  parcel  is  this  letter 
to  Collins  :  what  reason  the  Committee  have  for  supposing  this  letter 
belonged  to  the  parcel  they  do  not  say  :  they  do  not  even  say  whether 
it  was  a  separate  paper  or  not.  The  papers  of  dead  mathematicians, 
after  going  through  the  hands  of  executors,  are,  we  suspect,  not  always 
tied  up  exactly  in  the  order  they  were  untied.  Whether  the  parcel  is 
otherwise  known  to  have  found  its  way  to  Oldenburg  than  from  the  in- 
tention expressed  in  the  memorandum,  we  are  not  told — nor  whether 
Oldenburg  sent  it  to  Paris — nor  whether,  having  arrived  at  Paris,  it  was 
sent  on  to  Hanover ;  and  finally  they  state,  without  adding  how  they 
came  to  know  it,  that  it  was  sent  to  Leibniz  on  June  the  26th,  1676.  If 
the  letter  belonged  to  the  parcel,  and  if  the  parcel  were  sent  to  Olden- 
burg, and  if  Oldenburg  sent  it  to  Paris,  and  if  his  Paris  correspondent 
sent  it  to  Hanover,  and  if  it  arrived  safe,  and  if  Leibniz,  meaning  to 
make  an  unfair  use  of  it,  was  unwise  enough  to  return  this  evidence 
against  himself — the  case  of  the  Committee  is  good,  with  only  one  more 
if;  that  is,  if  the  letter  contained  anything  new  to  the  purpose,  which 
we  think  it  palpably  does  not.  That  is  to  say,  the  letter  itself  is  only 
what  any  strong  mathematician  might  have  drawn  from  Barrow  and 
Fermat,  who  are  almost  the  joint  inventors  of  Fluxions,  if  that  letter 
contained  them.  It  is  worth  the  remembering  that  Collins  was  not 
likely  to  tie  up  letters  miscellaneously  :  he  was  a  regular  accountant, 
a  methodical  writer  on  and  practiser  of  book-keeping,  and  a  man  of 
business.  For  aught  we  know,  he  may  lie  unquiet  in  his  grave  to  this 
day,  under  the  imputation  of  having  sent  a  parcel  which  contained  a 
paper  neither  mentioned  in  the  docket  nor  in  the  letter  of  advice. 
Perhaps  he  never  sent  it  at  all :  would  not  this  methodical  man  have 
written  on  the  parcel  the  date  of  its  return  ? 


30  NE  WTON 

and  others.  Leibniz  never  made  any  formal  answer, 
but  his  friends  retorted  the  charge  of  plagiarism 
upon  Newton,  and  John  Bernoulli  made  a  short 
anonymous  reply.  The  Committee,  content  perhaps 
with  the  number  of  those  who  were  ready  to  swear 
that  black  was  both  black  and  white,  and  neither, 
and  to  believe  it  too,  rather  than  yield  anything 
to  a  foreigner  (and  it  is  to  be  remembered  that 
Leibniz,  the  servant  of  the  Elector,  was  particularly 
obnoxious  to  all  the  Jacobites),  published  nothing 
further  :  the  Society  (May  the  2Oth,  1714),  in  refer- 
ence to  the  complaint  of  Leibniz  that  he  had  been 
condemned  unheard,  resolved  that  it  was  never 
intended  that  the  Report  of  the  Committee  should 
pass  for  a  decision  of  the  Society  :  but  others 
persisted  in  calling  it  so.  A  mutual  friend,  the 
Abb6  Conti,  being  in  England  in  1715,  Leibniz  at 
the  latter  end  of  that  year  wrote  him  a  letter,  in 
the  postscript  of  which  he  adverted  to  the  usage 
he  had  received.  This  letter  excited  curiosity  in 
London  :  and  Newton,  whose  power  in  matters  of 
science  was  then  kingly,  requested  and  obtained  the 
presence  of  all  the  foreign  ambassadors  at  the  Royal 
Society  to  collate  and  examine  the  papers.  After 
this  had  been  done,  Baron  Kirmansegger,  one  of  the 
ambassadors,  stated  his  opinion  that  the  dispute 
could  not  be  terminated  in  that  manner ;  that 
Newton  ought  to  write  to  Leibniz,  state  his  own 
case,  and  demand  an  answer.  All  present  agreed, 


NEWTON  31 

and  the  king  (George  I.),  to  whom  the  matter  was 
mentioned  that  same  evening,  was  of  the  same 
opinion.  Newton  accordingly  wrote  a  letter  to 
Conti,  in  which  he  relies  mostly  upon  what  Leibniz 
had  either  expressly  or  tacitly  admitted.  Nine 
times,  on  different  points,  he  calls  upon  Leibniz 
to  acknowledge  something  because  he  had  once 
acknowledged  it.  Leibniz  replied  at  great  length. 
Newton  did  not  rejoin,  except  in  notes  on  the  corre- 
spondence which  he  circulated  privately  among  his 
friends.  Leibniz  died  in  November  1716,  and 
Newton  forthwith  handed  the  whole  correspondence, 
with  his  final  notes,  to  Raphson,  whose  History  of 
Fluxions  was  then  in  process  of  printing.  The  book 
appeared  with  this  correspondence  as  an  appendix  : 
it  is  dated  1715,  but  the  publication  was  retarded. 
And  in  the  third  edition  of  the  Principia,  published 
in  1726,  Newton  omitted  the  scholium  we  have 
quoted  above,  in  spite  of  his  doctrine  that  what  was 
once  acknowledged  should  be  always  acknowledged. 
In  its  place  he  put  another  scholium,  with  a  similar 
beginning  and  ending,  but  referring  not  to  Leibniz 
but  to  his  own  letter  to  Collins  of  December  1672. 
In  the  Conti  correspondence — that  is,  in  the  notes 
which  he  would  not  print  while  Leibniz  was  alive — 
he  had  evaded  the  plain  meaning  of  this  scholium, 
asserting  that  it  was  not  an  admission,  but  a 
challenge  to  Leibniz  to  make  it  appear  that  the 
latter  had  the  priority  ;  and  further,  that  by  refer- 


32  NEWTON 

ring  to  the  letters,  he  left  the  reader  to  consult  them 
and  interpret  the  paragraph  thereby.  This  was  the 
climax  of  blind  unfairness  :  for  Newton  does  not 
specify  the  dates  of  the  letters,  and  gives  their 
description  wrongly  (for  they  were  written  to 
Oldenburg,  not  to  him).  And  further,  the  reader 
could  not  use  them,  for  they  were  not  published, 
nor  at  that  time  intended  for  publication. 

We  shall  presently  make  some  remarks  on  the 
conduct  of  Newton  in  this  transaction  ;  but  we  now 
proceed  to  the  merits  of  the  question.  That  Leibniz 
derived  nothing  from  Newton  except  the  knowledge 
that  Newton  could  draw  tangents,  find  maxima  and 
minima,  etc.,  by  some  organised  method,  we  have 
no  doubt  whatever,  nor  has  any  one  else,  at  this 
time,  so  far  as  we  know.  But,  though  we  may  be 
singular  in  the  opinion,  we  agree  with  Bernoulli  that 
Newton  did  derive  from  Leibniz  (without  being 
aware  of  the  extent  of  his  obligation,  we  think)  the 
idea  of  the  permanent  use  of  an  organized  mode  of 
mathematical  expression.  On  a  simple  question  of 
fact,  opinion  and  construction  apart,  we  take  the 
words  of  both  as  indisputable  ;  neither  would  have 
descended  to  bare  falsehood.  Now,  in  the  first  place, 
it  is  essential  to  observe  that  the  genius  of  Newton 
did  not  shine  in  the  invention  of  mathematical 
language :  and,  the  disputed  fluxions  apart,  he 
added  nothing  to  it.  The  notation  of  the  Principia 
is  anything  but  a  model.  We  know  by  the  letter  in 


NEWTON  33 

which  Leibniz  communicated  his  system  to  Newton, 
in  1677,  that,  at  that  period,  Newton  received 
communication  of  the  idea  of  an  organised  and 
permanent  language :  and  the  question  is  whether 
he  had  it  already.  From  his  own  Conti  correspond- 
ence, written  after  it  was  within  his  knowledge 
that  Bernoulli  had  asserted  him  to  have  taken  his 
idea  of  notation  from  Leibniz,  and  when  he  makes 
the  fullest  and  most  definite  assertions  as  to  the 
extent  to  which  he  has  carried  the  use'of  his  method, 
he  does  not  assert  that  before  receipt  of  Leibniz's 
letter  he  did  more  than  "  sometimes"  use  one  dot 
for  a  first  fluxion,  two  for  a  second,  and  so  on.1 
Neither  of  the  parties  knew  of  the  importance  which 
posterity  would  attach  to  this  simple  point  :  and  it 
is  our  full  conviction  that  Newton,  who  had  only 
got  the  length  of  finding  it  occasionally  convenient 
to  use  a  specific  language,  would  never  have 
organised  that  language  for  permanent  use  had  he 
not  seen  the  letter  of  Leibniz.  Even  as  late  as  the 
publication  of  the  Principia  he  has  no  better  con- 
trivance than  using  small  letters  to  represent  the 
fluxions  of  great  ones.  We  are  avowedly  express- 
ing, in  one  point,  our  low  estimate  of  Newton's 
power  :  and  we  believe  the  reason  to  have  been,  that 
he  did  not  cultivate  a  crop  for  which  he  had  no  use. 
He  who  can  make  existing  language  serve  his 

1  [We  know  from  Newton's  manuscripts  that  he  used  dots  as  early 
as  1665.     Cf.  the  Appendix  to  the  second  Essay,  below.] 

3 


34  NE  WTON 

purpose  never  invents  more  :  and  Newton  was  able  to 
think  clearly  and  powerfully  without  much  addition 
to  the  language  he  found  in  use.  The  Principia^ 
obscure  as  it  is,  was  all  light  in  Newton's  mind  ;  and 
he  did  not  attempt  to  conquer  difficulties  which  he 
never  knew.1 

VIII 

We  now  pass  on  to  the  third  period  of  Newton's 
life.  In  1694,  his  old  friend  Charles  Montague2 
(afterwards  Lord  Halifax)  became  Chancellor  of  the 

1  [On  the  genesis  and  development  of  the   ideas  of  Newton  and 
Leibniz  on  the  infinitesimal  calculus,  and  the   great  controversy,  see 
De  Morgan's  second  Essay,  below.] 

2  Montague   was    deeply   attached,    says    Sir   David    Brewster,    to 
Newton's  half-niece,  Catherine  Barton,  to  whom  he  left  a  large  part  of 
his  fortune.     Mrs  Barton,  to  use  Sir  D.  Brewster's  words,  "  though  she 
did  not  escape  the  censures  of  her  contemporaries,  was  regarded  by 
those  who  knew  her  as  a  woman  of  strict  honour  and  virtue."     Sir 
D.  Brewster,  who  copies  the  words  from  the  Biographia  Britannicat 
declines,  in  his  reverence  for  all  that  belonged  to  Newton  (a  feeling  with 
which  we  have  more  sympathy  than  our  readers  will  give  us  credit  for), 
to  state  the  whole  case.    After  the  death  of  Montague's  wife,  he  was 
disappointed  in  a  second  marriage  which  he   projected,    "which  was 
the  less  to  be  regretted  as  he  had  some  time  before  cast  his  eye  upon  a 
niece  of  his  friend  Sir  Isaac  Newton,  to  be  the  superintendent  of  his 
domestic  affairs.     This  gentlewoman  .   .  .  was  then  a  celebrated  toast, 
being  young,  beautiful,  and  gay,  so  that  she  did  not  escape  censure, 
which  was  however  passed  upon  her  very  undeservedly,  since  we  are 
well   assured   she   was  a   woman   of  strict  honour    and   virtue.     'Tis 
certain  she  was  very  agreeable   to  his  Lordship  in  every  particular." 
.  .  .  No  wonder  she  did  not  escape  censure,  especially  when  the  legacy 
left  by  Lord  Halifax  is  left,  to  use  his  own  words,  "  as  a  token  of  the 
sincere  love,  affection,  and  esteem  I  have  long  had  for  her  person,  and 
as  a  small  recompence  for  the  pleasure  and  happiness  I  have  had  in  her 
conversation."     And  all  this  from  an  apologist:   what,  then,  was  the 
truth?     On   reviewing  this  note,    we   think  it   right  to  add   that  the 
statement  that  there  were  feelings  of  love  between  the  parties  (which, 
if  true,  puts  their  relation  to  one  another  beyond  any  reasonable  doubt) 
is  not  from  the  author  here  cited,  but  from  Sir  D.  Brewster,  who  does 
not  give  his  authority.     [On  De  Morgan's  later  investigations  on  the 
relations  between  Catherine  Barton  and  Lord  Halifax,  see  the  third 
Essay,  below,  §  VII.,  and  the  notes  added  to  it] 


NEWTON  35 

Exchequer,  and  it  was  one  of  his  plans  to  restore 
the  adulterated  coinage.  He  served  both  his  friend 
and  his  plan  by  making  Newton  Warden  of  the  Mint, 
a  place  of  five  or  six  hundred  a  year  (March  the  iQth, 
1695  *)•  In  I^99>  Newton  was  made  Master  of  the 
Mint,  on  which  occasion  he  resigned  to  Whiston, 
as  his  deputy,  the  duties  and  emoluments  of  the 
Lucasian  professorship,  and  resigned  to  him  the 
professorship  itself  of  1703.  In  1701,  he  was  again 
elected  member  for  the  University  ;  but  he  was 
turned  out  by  two  sons  of  Lords  in  1705.  In  1703, 
he  was  chosen  President  of  the  Royal  Society,  and 
was  annually  re-elected  during  the  rest  of  his  life, 
In  1705,  he  was  knighted  at  Cambridge  by  Queen 
Anne.  In  1709,  he  entrusted  to  Roger  Cotes  the 
preparation  of  the  second  edition  of  the  Principia^ 
which  appeared  in  1713.  All  the  correspondence 
relating  to  the  alterations  made  in  this  edition  is  in 
the  Library  of  Trinity  College.2  In  1714,  at  the 
accession  of  George  I.,  he  became  an  intimate 
acquaintance  of  the  Princess  of  Wales  (wife  of 
George  II.),  who  was  also  a  correspondent  of 
Leibniz.  Some  observations  made  by  the  latter  on 
the  philosophy  of  Locke  and  of  Newton  brought  on 
the  celebrated  correspondence  between  Leibniz  and 
Clarke.  And  at  the  same  time,  an  abstract  of 
Newton's  ideas  on  chronology,  drawn  up  for  the 


1  [This  ought  to  be  1696.     See  note  on  p.  4.] 

2  [This  correspondence  was  published  by  Edleston  in  1850  (pp.  «V.).] 


36  NE  WTON 

Princess,  and  at  her  request  communicated  to  Conti, 
got  abroad  and  was  printed  at  Paris  :  on  which,  in 
his  own  defence,  he  prepared  his  large  work  on  the 
subject.  On  this  it  is  not  necessary  to  speak  :  his 
ideas  on  chronology,  founded  on  the  assumption  of 
an  accuracy  in  the  older  Greek  astronomers  which 
nobody  now  allows  them,  are  rejected  and  obsolete. 
But  the  work  does  honour  to  his  ingenuity  and  his 
scholarship,  showing  him  to  be  not  meanly  versed 
in  ancient  learning.  In  1726,  Dr  Pemberton  com- 
pleted, at  his  request,  the  third  edition  of  the 
Principia.  With  this  he  seems  to  have  had  little  to 
do,  for  his  health  had  been  declining  since  1722. 
He  was  relieved  by  gout  in  1725.  February  the 
28th,  1727,  he  presided  for  the  last  time  at  the 
Royal  Society.  He  died  of  the  stone  (so  far  as  so 
old  a  man  can  be  said  to  die  of  one  complaint)  on 
the  20th  of  March.  All  the  tributes  of  respect  to 
his  memory  belong  rather  to  the  biographies  of  those 
who  had  the  honour  to  pay  them  than  to  his  :  the 
gradual  reception  of  his  philosophy  throughout 
Europe  belongs  to  the  history  of  science.  We 
shall  now  offer  some  remarks  on  his  character  as  a 
philosopher  and  as  a  man. 

IX 

We  have  already  adverted  to  the  manner  in  which 
his    biographers    have    represented   him    to    be    as 


NEWTON  37 

much  above  ordinary  humanity  in  goodness  as 
in  intellectual  power.  That  his  dispositions  were 
generally  good  and  his  usual  conduct  in  the  relations 
of  life  admirable  to  an  extent  which  should  make 
his  worst  enemy,  if  he  had  any  regard  to  truth,  hand 
him  down  as  a  man  of  high  principle,  no  one  who 
knows  his  history  can  deny.  But  when  injustice 
is  not  merely  concealed  but  openly  defended  ;  when 
meanness  is  represented  as  the  right  of  a  great 
philosopher  ;  when  oppression  is  tolerated,  and  its 
victims  are  made  subjects  of  obloquy  because  they 
did  not  submit  to  whatever  Newton  chose  to  inflict ; 
— it  becomes  the  duty  of  a  biographer  to  bear  more 
hardly  upon  instances  of  those  feelings,  than,  had 
they  been  properly  represented,  would  have  been 
absolutely  necessary.  Nor  does  it  matter  anything 
in  such  a  case  that  the  instances  alluded  to  are  the 
exception  in  the  character  and  not  the  rule  ;  for- 
bearance and  palliation  are  so  much  of  injustice 
towards  the  injured  parties. 

The  great  fault,  or  rather  misfortune,  of  Newton's 
character  was  one  of  temperament  : 1  a  morbid  fear 
of  opposition  from  others  ruled  his  whole  life. 
When,  as  a  young  man,  proposing  new  views  in 
opposition  to  the  justly  honoured  authority  of 
Descartes  and  lesser  names,  he  had  reason  to  look 

1  [On  this  word,  Mrs  De  Morgan  (Memoir,  p  257)  remarked  :  "  My 
husband  always  used  this  word  for  what  I  should  call  original  character 
or  inborn  disposition."  Cf.  §  XII.  of  this  Essay  and  §§  VI.  and  XI. 
of  the  third  Essay.  ] 


38  NEWTON 

for  opposition,  we  find  him  disgusted  by  the  want 
of  an  immediate  and  universal  assent,  and  represent- 
ing, as  he  afterwards  said,  that  '  *  philosophy  was 
so  litigious  a  lady,  that '  a  man  might  as  well  be 
engaged  in  lawsuits  as  have  to  do  with  her.''  How 
could  it  be  otherwise  ?  What  is  scientific  investiga- 
tion except  filing  a  bill  of  discovery  against  nature, 
with  liberty  to  any  one  to  move  to  be  made  a  party 
in  the  suit  ?  Newton  did  not  feel  this  ;  and,  not 
content  with  the  ready  acceptance  of  his  views  by  the 
Royal  Society,  a  little  opposition  made  him  declare 
his  intention  of  retiring  from  the  field.  He  had  the 
choice  of  leaving  his  opponents  unanswered,  and 
pursuing  his  researches  ;  committing  it  to  time  to 
show  the  soundness  of  his  views.  That  this  plan 
did  not  suit  his  temper  shows  that  it  was  not  the 
necessity  of  answering,  but  the  fact  of  being 
opposed,  which  destroyed  his  peace.  And  he 
steadily  adhered,  after  his  first  attempt,  to  his 
resolution  of  never  willingly  appearing  before  the 
world.  His  several  works  were  extorted  from  him  ; 
and,  as  far  as  we  can  judge,  his  great  views  on 
universal  gravitation  would  have  remained  his  own 
secret  if  Halley  and  the  Royal  Society  had  not  used 
the  utmost  force  they  could  command.  A  discovery 
of  Newton  was  of  a  two-fold  character — he  made  it, 
and  then  others  had  to  find  out  that  he  had  made  it. 
To  say  that  he  had  a  right  to  do  this  is  allowable  ; 
that  is,  in  the  same  sense  in  which  we  and  our 


NE  WTON  39 

readers  have  a  right  to  refuse  him  any  portion  of 
that  praise  which  his  biographers  claim  for  him. 
In  the  higher  and  better  sense  of  the  word,  he  had 
no  right  to  claim  the  option  of  keeping  from  the 
world  what  it  was  essential  to  its  progress  that  the 
world  should  know,  any  more  than  we  should  have 
a  right  to  declare  ourselves  under  no  obligation  to 
his  memory  for  the  services  which  he  rendered.  To 
excuse  him,  and  at  the  same  time  to  blame  those 
who  will  not  excuse  him,  is  to  try  the  first 
question  in  one  court  and  the  second  in  another. 
A  man  who  could  write  the  Principia,  and  who 
owed  his  bread  to  a  foundation  instituted  for  the 
promotion  of  knowledge,  was  as  much  bound  to 
write  it  as  we  are  to  thank  him  for  it  when  written. 
When  he  was  young  and  comparatively  unknown, 
this  morbid  temperament  showed  itself  in  fear  of 
opposition  ;  when  he  became  king  of  the  world  of 
science  it  made  him  desire  to  be  an  absolute 
monarch ;  and  never  did  monarch  find  more  ob- 
sequious subjects.  His  treatment  of  Leibniz,  of 
Flamsteed,  and  (we  believe)  of  Whiston  is,  in  each 
case,  a  stain  upon  his  memory.  As  to  Leibniz,  it 
must  of  course  be  a  matter  of  opinion  how  far 
Newton  was  behind  the  scenes  during  the  concoction 
of  the  Commercium  Epistolicum  :  but  from  the 
moment  of  his  appearance  in  propria  persona,  his 
conduct  is  unjust.  Leibniz,  whose  noble  candour 
in  unfolding  his  own  discovery,  in  answer  to 


40  NE  WTON 

Newton's  a  b  c,  and  so  on,  must  have  been  felt  at 
the  time  as  a  stinging  reproof,  is  answered  with 
arrogance  (dignified  severity  is  the  other  name) 
and  treated  with  unfairness.  Nothing  can  excuse 
Newton's  circulating  his  reply  among  his  friends  in 
writing,  and  printing  it  when  he  heard  of  the  death 
of  Leibniz  :  this  conduct  tells  its  own  story  in 
unanswerable  terms.  And,  if  it  were  Newton's  own 
act  and  deed,  nothing  can  excuse  in  him  the 
omission  of  the  Scholium  from  the  third  edition, 
or  rather  the  alteration  of  it  in  such  manner  as  to 
resemble  the  former  one  in  its  general  tenor,  But, 
as  Newton  was  then  very  old,  and  as  he  had  allowed 
it  to  stand  in  the  second  edition,  published  when  the 
dispute  was  at  its  height,  it  is  possible  that  he  left 
the  matter  to  Dr  Pemberton,  the  editor,  or  some 
other  person. 

The  story  of  the  treatment  of  Flamsteed  has 
only  recently  become  known,  by  the  late  Mr  Baily's 
discovery  of  the  correspondence.  Flamsteed  was 
Astronomer  Royal,  and  his  observations  were  to  be 
printed  at  the  expense  of  the  Prince  Consort.  A 
Committee,  with  Newton  at  its  head,  was  to  super- 
intend the  printing.  If  we  took  Flamsteed's  word 
for  the  succession  of  petty  annoyances  to  which 
he  was  subject,  we  might  perhaps  be  wrong  ;  for 
Flamsteed  was  somewhat  irritable,  and  no  doubt  the 
more  difficult  to  manage  because  he  was  the  first 
observer  in  the  world,  and  not  one  of  the  Committee 


NEWTON  41 

was  an  observer  at  all  But  there  are  two  specific 
facts  which  speak  for  themselves.  The  catalogue  of 
stars  (Flamsteed's  own  property)  had  been  delivered 
sealed  up,  on  the  understanding  that  the  seal  was 
not  to  be  broken  unless  Flamsteed  refused  to  comply 
with  certain  conditions.  After  the  Prince  was  dead, 
and  the  trust  had  been  surrendered  (it  seems  to  have 
been  transferred  to  the  Royal  Society),  and  without 
any  notice  to  Flamsteed,  the  seal  was  broken,  with 
Newton's  consent,  and  the  catalogue  was  printed. 
Halley  was  exhibiting  the  sheets  in  a  coffee-house, 
and  boasting  of  his  correction  of  their  errors.  A 
violent  quarrel  was  the  consequence,  and  a  scene 
took  place  on  one  occasion  at  the  Royal  Society 
which  we  cannot  discredit  (for  Flamsteed's  character 
for  mere  truth  of  narration  has  never  been  success- 
fully impugned,  any  more  than  Newton's),  but  which 
most  painfully  bears  out  our  notion  of  the  weak 
point  of  Newton's  character.  As  to  the  breaking  of 
the  seal  Newton  pleaded  the  Queen's  command — an 
unmanly  evasion,  for  what  did  the  Queen  do  except 
by  advice  ?  who  was  her  adviser  except  the  President 
of  the  Royal  Society?  Shortly  afterwards  the 
second  edition  of  the  Principia  appeared.  Flam- 
steed,  whose  observations  had  been  of  more  service 
to  Newton  than  those  of  any  other  individual,  and 
to  whom  proper  acknowledgment  had  been  made 
in  the  first  edition,  and  who  had  increased  the 
obligation  in  the  interval,  had  his  name  erased  in  all 


42  NEWTON 

the  passages  in  which  it  appeared  (we  have  verified, 
for  this  occasion,  eight  or  nine  places  ourselves).1 
To  such  a  pitch  is  this  petty  resentment  carried, 
that  whereas  in  one  place  of  the  first  edition  (prop. 
1 8,  book  III.)  there  is,  in  a  parenthesis,  "by  the 
observations  of  Cassini  and  Flamsteed  "  ;  the  corre- 
sponding place  of  the  second  is,  "  by  the  consent  of 
the  observations  of  astronomers." 

There  is  a  letter  of  Newton  to  Flamsteed  (January 
the  6th,  1699),  written  before  they  were  in  open 
rupture,  containing  an  expression  which  has  excited 
much  surprise  and  some  disapprobation.  Flamsteed 
having  caused  a  published  reference  to  be  made  to 
Newton's  continuation  of  his  lunar  researches,  the 
latter  says,  ' ' I  do  not  love  to  be  printed  on  every 
occasion,  much  less  to  be  dunned  and  teased  by 
foreigners  about  mathematical  things,  or  to  be 
thought  by  your  own  people  to  be  trifling  away  my 
time  when  I  should  be  about  the  King's  business." 
This  letter  was  not  intended  for  publication,  still  less 
for  posterity  :  the  phrase  was  pettish,  unworthy  even 
of  Newton  in  a  huff.  But  the  feeling  was  the  right 
one.  If  there  were  any  thing  unworthy  of  the 
dignity  of  Newton,  it  was  in  taking  a  place  which 
required  him  to  give  up  the  glorious  race  in  which 

1  [This  is  not  quite  correct.  Edleston  (pp.  cit.,  p.  Ixxv)  also  questions 
very  much  whether  the  suppression  of  Flamsteed's  name  in  several 
places  where  it  had  appeared  in  the  final  edition  was  not  such  as  was 
necessary  in  the  process  of  improving  the  work.  Newton's  own  experi- 
ments on  the  old  echo  in  Trinity  College  cloister  gave  way,  in  the 
second  edition,  to  more  accurate  researches.] 


NEWTON  43 

he  had  outstripped  all  men,  and  the  researches  which 
were  for  him  alone,  while  the  regulation  of  the  Mint 
was  not  above  the  talents  of  thousands  of  his  country- 
men. But,  having  taken  it,  it  was  his  duty  to  attend 
to  it  in  the  most  regular  and  conscientious  manner, 
as  in  fact  he  did  to  the  end  of  his  days.  His  con- 
temporary Swift  had  the  sense  to  refuse  the  troop 
of  dragoons  which  King  William  offered  him  before 
he  took  orders :  it  would  have  been  better  for 
Newton's  fame  if  he  had  left  all  the  coinage,  clipped 
and  undipped,  to  those  who  were  as  well  qualified 
as  himself.  His  own  share  might  not  have  been  so 
large,1  but  money  was  not  one  of  his  pursuits.  He 
was  nobly  liberal  with  what  he  got,2  particularly  to 
his  own  family  :  and  it  may  be  added  that  the 
position  of  his  family,  which  was  far  from  well  off 
in  the  world,  is  the  only  circumstance  which  can 
palliate  his  giving  up  the  intellectual  advancement 

1  Sir  D.  Brewster  represents  Newton  as  having  a  very  scanty  income 
before  he  gained  his  office  in  the  Mint.     But  in  fact  he  had  from  his 
College  board  and  lodging  (both  of  the  best)  and  the  stipend  of  his 
fellowship :   from  the  University  the  salary  of  his  professorship :  and 
from   his   patrimony  about  ;£ioo  a   year.     He  could   not   have   had 
less  than  ^"250  a  year  over  and  above  board  and  lodging  :  which,  in 
those   days,  was  a  very  good   provision   for   an   unmarried  man,  and 
would  not  be  a  bad  one  now. 

2  [Here   we  may  mention  that  Pemberton  is  said  to  have  received 
two  hundred  guineas  for  his  service  in  editing  the  third  edition  of  the 
Principia  (Brewster,  Memoirs,   1855,  vol.   i,   p.   318).     For  making  a 
Latin  translation  of  the  Optics,  Samuel  Clarke  and  his  children  received 
five  hundred  pounds  (ibid. ,  p.  248).     Cf.  ibid.,  vol.  ii,  pp.  411-413, 
for  other  instances  of  Newton's  sometimes  rather  careless  generosity. 
Further,  on  July  the  I3th,  1719,  Newton  gave  to  Pound,  the  astronomer, 
probably  in  acknowledgment  of  astronomical  observations  supplied  by 
him  for  the  Principia,  a  "free  gift"  of  fifty  guineas.     On  April  the 
28th,  1720,  Pound  recorded  another  gift  from  Newton  of  fifty  guineas. 
This  generosity  does  not  appear  in  his  treatment  of  rivals.] 


44  NEWTON 

of  all  men,   ages,   and  countries,  to  trifle  away  his 
time  about  the  King's  business.1 

His  treatment  of  Whiston,  as  published  in  the 
autobiography  of  the  latter,2  was  always  disregarded, 
as  the  evidence  of  a  very  singular  person.  Standing 
alone — for  his  conduct  to  Leibniz  was  defended  by 
national  feeling,  and  his  treatment  of  Flamsteed 
was  unknown  —  it  never  carried  much  weight. 
Whiston  had  excessive  vanity  and  a  peculiar  fana- 
ticism of  his  own  invention,  which  were  sure  to  be 
made  the  most  of ;  for  a  man  who  loses  his  pre- 
ferment for  his  conscience  had  need  be  perfect,  if 
he  would  escape  those  who  think  him  a  fool,  and 
those  who  feel  him  a  rebuke.  And  in  Whiston's 
day  the  number  was  not  small  of  the  clergy  who 
disavowed  the  articles  to  which  they  had  sworn, 
without  even  having  the  decency  to  provide  a  non- 
natural  sense.  Newton  refused  him  admission  into 
the  Royal  Society,  declaring  that  he  would  not 
remain  president  if  Whiston  were  elected  a  fellow, 
A  reason  is  asserted  for  this  which  we  shall  presently 
notice  ;  but  Whiston's  account  is  as  follows.  After 
alluding  to  Newton  having  made  him  his  deputy, 
and  then  his  successor,  he  adds  :  '  *  So  did  I  enjoy 
a  large  portion  of  his  favour  for  twenty  years  to- 
gether. But  he  then  perceiving  that  I  could  not 

1  [-For   Brewster's   version  of  the  Flamsteed  episode,  see  Memoir -s, 
1855,  vol.  ii,  pp.  157-242.] 

2  [Memoirs  of  the  Life  of  Mr  William  Whiston  by  himself,  London, 

I749-] 


NEWTON  45 

do  as  his  other  darling  friends  did — that  is,  learn 
of  him  without  contradicting  him  when  I  differed 
in  opinion  from  him, — he  could  not  in  his  old  age 
bear  such  contradiction  ;  and  so  he  was  afraid  of  me 
the  last  thirteen  years  of  his  life.  He  was  of  the 
most  fearful,  cautious,  and  suspicious  temper  that 
I  ever  knew." 

It  would  have  been  more  pleasant  merely  to 
mention  these  things  as  what  unfortunately  cannot 
be  denied,  than  to  bring  them  forward  as  if  it  were 
our  business  to  insist  upon  them.  But  the  manner 
in  which  the  biography  of  Newton  is  usually  written 
leaves  us  no  alternative.  We  are  required  to  worship 
the  whole  character,  and  we  find  ourselves  unable 
to  do  it.  We  see  conduct  defended  as  strictly 
right,  and  therefore,  of  course,  proposed  for  imita- 
tion, which  appears  to  us  to  be  mean,  unjust,  and 
oppressive.  As  long  as  Newton  is  held  up  to  be 
the  perfection  of  a  moral  character,  so  long  must 
we  insist  upon  the  exceptional  cases  which  prove 
him  to  have  been  liable  to  some  of  the  failings  of 
humanity.  But  to  those  who  can  fairly  admit  that 
his  conduct  is  proof  of  an  unhappy  temper  which 
sometimes  overcame  his  moral  feeling,  and  who 
therefore  look  for  the  collateral  circumstances  which 
are  to  excuse  or  aggravate,  there  are  various  con- 
siderations which  must  not  be  left  out  of  sight. 

In  the  first  place,  this  temperament  of  which  we 
have  given  instances,  is  of  all  others  the  one  which 


46  NE  WTON 

occasionally  lessens  the  control  of  the  individual 
over  his  own  actions.  Every  one  knows  how  apt 
we  are,  from  experience,  to  think  of  insanity  as  the 
possible  termination  of  the  morbidly  suspicious 
habit.  That  the  report  which  arose  about  Newton's 
mind  was  much  assisted  by  a  knowledge  of  this 
habit  existing  in  him,  we  have  little  doubt  :  for 
we  see,  in  our  own  day,  how  corroborative  such  a 
temper  is  held  to  be  of  any  such  rumour.  In  one 
instance,  and  in  illness  of  a  serious  character,  it  did 
take  a  form  which  we  can  hardly  hold  consistent 
with  sanity  at  the  time.  He  spoke  severely  of 
Locke,  his  old  and  tried  friend  (in  1693),  being  under 
the  apprehension  that  Locke  had  endeavoured  to 
' '  embroil  him  with  women  and  by  other  means  "  ; 
he  thought  there  was  a  design  to  ' '  sell  him  an 
office  and  to  embroil  him."  For  these  suspicions  he 
wrote  a  letter,  worthy  of  himself,  asking  pardon, 
and  saying  also  that  he  had  been  under  the  im- 
pression that  there  was  an  evil  intention,  or  ten- 
dency at  least,  in  some  of  Locke's  writings.  The 
latter,  in  an  affectionate  answer,  desired  to  know 
what  passages  he  alluded  to  ;  and  the  rejoinder  was 
that  the  letter  was  written  after  many  sleepless 
nights,  and  that  he  had  forgotten  what  he  said.  As 
we  have  only  the  letters  and  no  further  information, 
we  must  decide  as  we  can  whether  Newton  did 
really  express  himself  to  others  as  he  said  he  had 
done,  or  whether  he  only  fancied  it.  In  either  case 


NE  WTON  47 

there  is,  under  illness,  that  morbid  imagination  of 
injury  done  or  meditated,  which  seems  to  have  been 
but  the  exaggeration  of  an  ordinary  habit.  If  we 
thought,  from  the  evidence,  that  Newton  had  ever 
been  insane,  we  should  see  no  reason  whatever  for 
concealing  our  opinion  :  we  do  not  think  so  ;  but 
we  think  it  likely  that  if  his  years  from  1660  to 
1680  had  been  passed  in  the  excesses  of  the 
licentious  court  of  his  day,  instead  of  the  quiet 
retirement  of  his  college,  there  might  have  been 
another  story  to  tell. 

Next,  it  is  not  fair  to  look  upon  the  character 
of  any  man,  without  reference  to  the  notions  and 
morals  of  his  time.  Take  Newton  from  his  pinnacle 
of  perfection,  from  the  background  of  the  picture, 
from  the  incidents  of  the  era  of  political  and  social 
profligacy  in  which  he  lived,  and  his  relative  char- 
acter then  seems  to  be  almost  of  the  moral  magni- 
ficence which  is  made  its  attribute.  Let  the  sum 
total  of  his  public  career  be  compared  with  that  of 
others  who  were  "about  the  King's  business,"  and 
we  cannot  help  looking  upon  the  honest  and  able 
public  servant,  who  passed  a  life  in  the  existing 
corruption  of  public  affairs  without  the  shadow  of  a 
taint  upon  his  official  morals,  with  an  admiration 
which  must  tend  to  neutralise  the  condemnation  we 
may  not  spare  upon  some  incidents  of  his  scientific 
life.  Further,  the  idolatrous  respect  in  which  he 
was  held  at  the  Royal  Society,  and  the  other  haunts 


48  NE  WTON 

of  learning — the  worship  his  talents  received  at 
home  and  abroad,  from  Halley's1  "nee  fas  est 
propius  mortali  attingere  divos,"  to  de  PHopital's 
almost  serious  question  whether  Newton  ate,  drank, 
and  slept — the  investment  of  his  living  presence 
with  all  the  honours  once  paid  to  the  memory  of 
Aristotle — make  it  wonderful,  not  that  he  should 
sometimes  have  indulged  an  unhappy  disposition, 
but  that  he  should  have  left  so  few  decided  instances 
of  it  on  record.  That  both  his  person  and  his 
memory  were  held  dear  by  his  friends  there  is  no 
doubt  :  this  could  not  have  been  unless  the  cases 
we  have  cited  had  been  exceptions  to  the  tenor  of 
his  conduct  ;  and,  knowing  the  disposition  of  which 
we  have  spoken  to  be  one  against  which  none  but 
a  high  power  can  prevail,  we  are  to  infer  that  it  was, 
in  general,  heartily  striven  against  and  successfully 
opposed. 2 

X 

The  mind  of  Newton,  as  a  philosopher,  is  to  this 
day,  and  to  the  most  dispassionate  readers  of  his 
works,  the  object  of  the  same  sort  of  wonder  with 
which  it  was  regarded  by  his  contemporaries.  We 
can  compare  it  with  nothing  which  the  popular 
reader  can  understand,  except  the  idea  of  a  person 

1  "  Nor  is  it  possible  for  man  to  be  nearer  to  God  " :  the  last  line  of 
Halley's  verses  on  the  Principia. 

2  [For  De  Morgan's  view  of  Newton's  character,  see  also  end  of  §§  II 
and  VI.  of  the  third  Essay,  below.] 


NE  WTON  49 

who  is  superior  to  others  in  every  kind  of  athletic 
exercise ;  who  can  outrun  his  competitors  with  a 
greater  weight  than  any  one  of  them  can  lift  standing. 
There  is  a  union,  in  excessive  quantity,  of  different 
kinds  of  force :  a  combination  of  the  greatest 
mathematician  with  the  greatest  thinker  upon  ex- 
perimental truths  ;  of  the  most  sagacious  observer 
with  the  deepest  reflecter.  Not  infallible,  but  com- 
mitting, after  the  greatest  deliberation,  a  mistake 
in  a  simple  point  of  mathematics,  such  as  might 
have  happened  to  any  one  :  yet  so  happy  in  his 
conjectures,  as  to  seem  to  know  more  than  he 
could  possibly  have  had  any  means  of  proving. 
Carrying  his  methods  to  such  a  point  that  his  im- 
mediate successors  could  not  clear  one  step  in  ad- 
vance of  him  until  they  had  given  the  weapons  with 
which  himself  and  Leibniz  had  furnished  them  a 
completely  new  edge,  yet  apparently  solicitous  to 
hide  his  use  of  the  most  efficient  of  these  weapons, 
and  to  give  his  researches  the'  appearance  of  having 
been  produced  by  something  as  much  as  possible 
resembling  older  methods.  With  few  advantages 
as  a  writer  or  a  teacher,  he  wraps  himself  in  an 
almost  impenetrable  veil  of  obscurity,  so  as  to 
require  a  comment  many  times  the  length  of  the 
text  before  he  is  easily  accessible  to  a  moderately 
well-informed  mathematician.  He  seems  to  think 
he  has  done  enough  when  he  has  secured  a  possibil- 
ity of  rinding  one  reader  who  can  understand  him 

4 


50  NE  WTON 

with  any  amount  of  pains  :  as  if,  seeing  Halley  to 
be  of  all  men  he  knew  next  to  himself  in  force,  he 
had  determined  that  none  but  Halley  at  his  utmost 
stretch  of  thought  should  follow  him.  Accordingly 
one,  to  whom  in  his  later  years  he  used  to  send 
inquirers,  saying,  "Go  to  Mr  De  Moivre,  he  knows 
these  things  better  than  I  do,"  avowed  that  when 
he  saw  the  Principia  first,  it  was  as  much  as  he 
could  do  to  follow  the  reasoning.  It  would  be 
difficult  to  name  a  dozen  men  in  Europe  of 
whom,  at  the  appearance  of  the  Principia,  it  can 
be  proved  that  they  both  read  and  understood  the 
work. 

Newton  himself  attributed  all  his  success  to 
patience  and  perseverance  more  than  to  any  peculiar 
sagacity  :  but  on  this  point  his  judgment  is  worth 
nothing.  Unquestionably,  he  had  the  two  first  in 
an  enormous  degree,  as  well  as  the  third  ;  nor  is  it 
too  much  to  say  that  there  is  no  one  thing  in  his 
writings  which  the  sagacity  of  some  of  his  contem- 
poraries might  not  have  arrived  at  as  well  as  his  own. 
But  to  make  an  extensive  system  many  things  are 
necessary  :  and  one  point  of  failure  is  fatal  to  the 
whole.  Again,  it  is  difficult  to  put  before  the 
ordinary  reader,  even  if  he  be  a  mathematician,  a 
distinct  view  of  the  merit  of  any  step  in  the  forma- 
tion of  a  system.  Unless  he  be  acquainted  with 
the  history  of  preceding  efforts,  he  comes  to  the 
consideration  of  that  merit  from  the  wrong  direction  ; 


NE  WTON  5 1 

for  he  reads  the  history  from  the  end.  He  goes  to 
the  mail-coach,  back  from  the  railroad  instead  of 
forward  from  the  old  strings  of  pack-horses  :  from 
a  macadamised  road  lighted  with  gas  to  the  rough 
stones  and  the  oil-lamps,  instead  of  beginning  with 
the  mud  and  the  link-boys.  Perhaps  the  same  sort 
of  wrong  judgment  may  accompany  the  retrospect  of 
its  own  labours  in  a  mind  like  Newton's  ;  causing  it 
to  undervalue  the  intellectual  part  of  which,  in  any 
case,  it  is  least  capable  of  judging. 

The  world  at  large  expects,  in  the  account  of  such 
things,  to  hear  of  some  marvellous  riddles  solved, 
and  some  visibly  extraordinary  feats  of  mind.  The 
contents  of  some  well-locked  chest  are  to  be  guessed 
at  by  pure  strength  of  imagination  :  and  they  are 
disappointed  when  they  find  that  the  wards  of  the 
lock  -were  patiently  tried,  and  a  key  fitted  to  them 
by  (it  may  be  newly  imagined)  processes  of  art. 
Thus  the  great  experiment,  the  trial  of  the  moon's 
gravitation,  seems  wonderfully  simple  to  those  who 
have  to  describe  it ;  precisely  what  anybody  could 
do.  If  the  moon  were  not  retained  by  some  force, 
she  would  proceed  in  a  straight  line  MB  :l  some- 
thing causes  her  to  describe  MA  instead,  which  is 
equivalent  to  giving  a  fall  of  BA  towards  the  earth. 
Now  since  EM,  the  distance  of  the  moon  from  the 
earth's  centre,  is  about  60  times  EC,  the  earth's 

1  [This  refers  to  a  simple  figure  which  it  is  not  necessary  to  reproduce 
here,  as  anybody  can  reproduce  it  for  himself  from  what  is  said  in  the 
text.] 


52  NEWTON 

radius,  it  follows  that  if  there  be  gravitation  at  the 
moon,  and  if  it  diminish  as  the  square  of  the  distance 
increases,  it  ought  to  be  60  times  60,  or  3600  times 
as  great  at  the  surface  of  the  earth  as  at  M  ;  or  a 
body  at  the  earth's  surface  ought  to  fall  in  one 
minute  3600  times  as  much  as  BA  (supposing  MA 
to  be  the  arc  moved  over  in  one  minute).  A 
surveyor's  apprentice,  even  in  Newton's  day,  could 
with  great  ease  have  ascertained  that  such  is  the 
fact,  if  the  data  had  been  given  to  him.  Now  why 
was  Newton  the  first  to  make  this  simple  trial  ? 
The  notion  of  gravitation  was,  as  we  have  said, 
afloat :  and  Bouillaud  had  declared  his  conviction 
that  attractive  forces,  if  they  exist,  must  be  inversely 
as  the  squares  of  the  distances.  Did  he  try  this 
simple  test  ?  Perhaps  he  did,  and  threw  away  his 
result  as  useless,  not  being  able  to  make  the  next 
step.  Or  was  it  that  neither  he  nor  any  one  except 
Newton  had  any  distinct  idea  of  measuring  from  the 
centre  of  the  earth  ?  If  so,  then  Newton  was  in 
possession  of  what  he  afterwards  proved,  namely, 
that  a  spherical  body,  the  particles  of  which  attract 
inversely  as  the  squares  of  the  distances,  attracts  as 
if  all  its  particles  were  collected  in  its  centre.1  In 
either  case,  this  may  serve  to  illustrate  what  a 
popular  reader  would  hardly  suppose,  namely,  that 
the  wonder  of  great  discoveries  consists  in  there 

1  [Newton  explicitly  stated  that  he  only  discovered  this  theorem  in 
1685;  cf.  above,  note  30.] 


NEWTON  53 

being  found  one  who  can  accumulate  and  put 
together  many  different  things,  no  one  of  which 
is,  by  itself,  stupendous  after  the  fact,  nor  calculated 
to  produce  that  sort  of  admiration  with  which  the 
whole  is  regarded. 

XI 

We  have  not  yet  mentioned  the  theological  writings 
of  Newton,  as  his  discussion  of  the  prophecies  of 
Daniel,  and  so  on.  About  his  opinions  on  this  sub- 
ject there  is  a  little  controversy  :  and  the  various 
sects  of  opinion  are  in  the  habit  of  opposing  to  each 
other  the  great  names  which  are  on  their  several 
sides  of  the  question.  That  Newton  was  a  firm 
believer  in  Christianity  as  a  revelation  from  God,  is 
very  certain  :  but  whether  he  held  the  opinions  of 
the  majority  of  Christians  on  the  points  which 
distinguish  Trinitarians  from  Arians,1  Socinians,  and 
Humanitarians,  is  the  question  of  controversy.  It 
is  to  be  remembered  that  during  the  whole  of 
Newton's  life  the  denial  of  the  doctrine  of  the 
Trinity  was  illegal,  the  statute  of  King  William 
(which  relaxed  the  existing  law,  for  a  man  was 

1  These  names  are  bandied  about  in  vituperative  discussions,  until 
they  are  so  misused  that  the  chances  are  many  readers  will  need  explana- 
tion of  them.  An  Arian  believes  in  the  finite  pre-existence  of  Jesus 
Christ,  before  his  appearance  on  earth  :  a  Socinian  believes  him  to  be  a 
man  who  did  not  exist  before  his  appearance  on  earth,  but  who  is  still 
a  proper  object  of  prayer  :  a  Humanitarian,  with  all  others  who  come 
under  the  general  name  of  Unitarian  (the  personal  unity  of  the  Deity 
being  a  common  tenet  of  all),  believes  him  to  be  a  man,  and  not  an 
object  of  prayer. 


54  NE  WTON 

hanged  in  1696  for  denying  the  Trinity)  making 
it  incapability  of  holding  any  place  of  trust  for  the 
first  offence,  and  three  years'  imprisonment  with 
other  penalties  for  the  second.  Few  therefore  wrote 
against  the  Trinity,  except  either  as,  in  the  Unitarian 
Tracts,  without  even  a  printer's  name,  or  evasively, 
by  arguing  against  the  Trinity  being  an  article  of 
faith,  that  is,  a  necessary  part  of  a  Christian's  hope 
of  salvation.  Premising  this,  we  take  the  evidence, 
as  it  stands,  for  and  against  the  heretical  character 
of  Newton's  opinions. 

There  is  a  widespread  tradition  that  Horsley 
objected  to  publish  a  part  of  the  "  Portsmouth 
Papers "  on  account  of  the  heresy  of  the  opinions 
contained  in  them  ;  which  statement  used  to  be 
even  in  children's  books,  and  was  made  by  Dr 
Thomson  in  his  History  of  the  Royal  Society.  These 
papers  have  never  been  published,  nor  has  any  one 
of  those  who  have  had  access  to  them  denied  the 
rumour  on  his  own  knowledge.  The  refusal  of 
Horsley  is  not  conclusive  in  itself;  because,  to 
use  the  words  of  one  of  the  children's  books  we 
remember  (called  a  ''British  Plutarch,"  or  some 
such  name),  he  was  a  "  rigid  high  priest,"  and 
heterodoxy  short  even  of  Arianism  would  probably 
have  led  him  to  such  a  determination.  But  the 
suppression  still  continues,  long  after  the  above 
rumour  has  been  very  effective  in  aiding  the  prob- 
abilities drawn  from  other  sources,  that  Newton's 


NEWTON  55 

opinions  were  even  more  heterodox  than  Arianism  ; 
and  there  is  some  force  in  this. 

Two  witnesses  from  among  Newton's  personal 
friends,  Whiston,  an  Arian  (calling  himself  a 
Eusebian),  and  Hopton  Haynes,  who  was  employed 
under  him  in  the  Mint,  and  who  was  a  Humanitarian, 
severally  bear  testimony  to  his  having  held  their 
several  opinions.  Whiston,  whose  intimate  acquaint- 
ance with  him  terminated  some  time  before  1720, 
states  in  two  places  that  Newton  was  a  Eusebian 
(Arian)  and  a  Baptist,  and  that  he  was  "  inclined  to 
suppose  "  these  two  sects  to  be  the  two  witnesses 1 
mentioned  in  the  book  of  Revelations.  Haynes2 
declares  him  to  have  been  a  Humanitarian,  and 
stated  that  he  much  lamented  that  his  friend  Dr 
Clarke  had  stopped  at  Arianism.  On  the  other 
hand,  the  writer  in  the  Biographia  Britannicay  who 

1  This  is  strange  ;  and  if  such  had  been  Whiston's  own  opinion,  we 
should  not  have  hesitated  to  conclude  that  he  had  misinterpreted  some 
civil  decliner  of  controversy.     But  Whiston  expressly  states  himself  to 
have  no  such  opinion.     That  he  would  intentionally  utter  a  falsehood  we 
believe  to  be  out  of  the  question. 

2  The  testimony  of  Whiston  is  in  his  Memoirs :  that  of  Haynes  is  less 
direct.     The  Unitarian  minister,  Richard  Baron,  who  was  a  friend  of 
Haynes,  states  the  preceding  as  having  passed  in  conversation  between 
him  and  Haynes.     The  statement  is  made  in  the  preface  of  the  first 
volume  of  his  collection  of  tracts,  called  A  Cordial  for  Low  Spirits 
(three  volumes,  London,   1763,  third  edition,  I2mo),  published  under 
the  name  of  Thomas  Gordon.     This  is  not  primary  evidence  like  that 
of  Whiston  ;   and  it   loses  force  by  the  circumstance  that  in  the  pos- 
thumous work  which  Mr  Haynes  left  on  the  disputed  points  (and  which 
was   twice   printed)  there  is  no  allusion   to  it.     But  those  who  weigh 
testimony  will  of  course  take  into  continued  consideration  its  amount  of 
corroborative  force.     And  a  great  many  writers  on  the  Antitrinitarian 
side  deserve  blame  for  not  stating  distinctly  that  it  is  only  a  testimony 
to  a  testimony  :  Baron  was  a  man  against  whose  character  for  truth  we 
never  heard  anything,  but  the  chances  of  misapprehension  increase  very 
rapidly  with  the  number  of  steps,  in  the  communication  of  oral  tradition. 


56  NEWTON 

cites  the  last  edition1  (1753)  of  Whiston's  Memoirs, 
says  that  Whiston  states  that  Newton  was  so  much 
offended  with  him  for  having  represented  him  as  an 
Arian,  that  this  was  the  reason  why  he  would  never 
consent  to  his  admission  into  the  Royal  Society. 
The  edition  of  1749,  thirteen  years  after  Newton's 

1  Though  aware  that  we  should  have  many  results  of  bias  to  encounter, 
we  had  hoped  that  we  should  have  got  through  our  task  without  having 
to  expose  absolute  and  fraudulent  falsification.  Since  writing  what  is  in 
the  text,  we  have  obtained  the  loan  of  the  edition  of  1753,  which  is 
scarce  compared  with  that  of  1749.  The  Biogr.  Brit,  informs  us 
(p.  3241)  that  in  pages  178,  249,  250  of  Whiston's  Memoirs,  edition 
of  1753,  8vo,  we  shall  find  the  justification  of  these  words:  "Mr 
Whiston,  who  represented  Sir  Isaac  as  an  Arian,  which  he  so  much 
resented  that  he  would  not  suffer  him  to  be  a  member  of  the  Royal 
Society  while  he  was  President."  We  look,  and  in  p.  178  we  find  that 
Whiston  states  Newton  to  be  an  Arian,  and  in  pp.  249  and  250  we  find 
that  Newton  excluded  Whiston  from  the  Royal  Society,  for  which  the 
reason  Whiston  gives  is  that  Newton  could  not  bear  contradiction,  in 
the  words  we  have  quoted  in  another  part  of  this  article.  The  biographer 
distinctly  implies  that  he  is  giving,  not  his  own  reason,  but  Whiston's 
reason.  And,  having  diligently  compared  the  editions  of  1749  and 
1753  (tne  latter  of  which  had  some  additions,  by  which  the  false  biographer 
hoped  to  gain  credit  from  those  who  looked  at  the  former),  we  find  that 
the  paragraphs  cited  only  differ  as  follows:  In  the  first,  1749  has 
Revelation,  1753  has  Revelation.  The  former  has  "and  friendly 
address  to  the  Baptists"  (pp.  14,  15),  which  the  latter  has  not.  In 
the  second,  1749  has  "desire  "  and  1753  has  ' '  desires  "  (a  little  instance, 
by  the  way,  of  the  disappearance  of  the  old  English  subjunctive),  and 
the  former  has  "through  confutation,"  when  the  latter  has  "thorough 
confutation."  Sir  D.  Brewster  (p.  284)  has  copied  the  false  biographer 
without  verifying  the  reference — a  common,  but  a  dangerous  practice. 
It  was  a  mere  accident  that  we  went  to  the  Biogr.  Brit.,  for  we 
distrust  it  from  old  acquaintance  on  all  matters  connected  with  Newton. 
We  do  not  know  at  this  moment  that  the  false  biographer,  as  we  call 
him,  is  the  original  falsifier  :  but  he  must  bear  the  blame  for  the  present. 
We  might  have  had  to  leave  the  explanation  to  Sir  D.  Brewster  :  for  he 
who  copies  a  reference  without  verification,  and  without  stating  that  he 
copies,  must  take  the  responsibility  of  that  reference.  But  as  it  stands, 
we  need  not  say  that  Sir  D.  Brewster  is  as  clear  in  this  instance  from 
the  imputation  of  intentionally  misleading  his  reader,  as  those  could 
wish  who  respect  his  character  and  admire  his  labours :  among  the 
number  of  whom  we  desire  to  place  ourselves.  And  his  candour  wiil 
lead  him  to  acknowledge  that  he  has  had  a  happy  escape  from  an 
imminent  danger  of  misconstruction,  with  no  blame  to  those  who 
made  it. 


NEWTON  57 

death,  shows  that  Whiston  had  then  no  such  know- 
ledge of  the  cause.  But,  if  it  were  so,  and  Haynes's 
testimony  be  true,  he  might  have  had  Priestley's 
objection  to  Arianism  rather  than  Horsley's  :  and  in 
either  case,  we  know  enough  of  Newton  to  be  sure 
that  he  would  be  likely  to  take  offence  at  any  talk 
about  opinions  he  did  not  choose  to  avow,  particu- 
larly such  as  were  illegal ;  and  above  all,  he  would 
fear  the  tongue  of  a  man  like  Whiston,  all  honesty 
and  no  discretion,  who  told  the  world  long  before 
his  death  all  that  he  knew  about  himself  and  every- 
body else,  without  the  least  reserve. 

Newton  wrote  (about  1690),  under  the  title  of 
"  Historical  Account  of  two  Notable  Corruptions  of 
Scripture,"  against  the  genuineness  of  two  passages 
on  which  Trinitarian l  writers  then  placed  much 
reliance  :  that  is,  against  the  genuineness  of  i  John 
v.  7,  and  that  of  the  word  0eo?  (God),  I  Timothy 
iii.  1 6.  Now,  though  Trinitarians  have  often  aban- 
doned the  first  passage,  and  given  up  the  Protestant 
reading  of  the  second,  it  has  rarely  happened, 
if  ever,  that  they  have  written  expressly  against 
them  :  the  world  at  large  sees  no  difference  between 
opposing  an  argument,  and  opposing  the  conclusion  ; 
and  parties  in  religion  and  politics  require 2  assent, 

1  Protestant   writers,    we    mean ;    the    reading    contended    for    by 
Newton  in  the  second  instance  has  been  that  of  Catholics  from    the 
time  of  Jerome. 

2  Dr  Chalmers,  for  example,  states  Newton  to  have  "abetted"  the 
leading  doctrine  of  the  Unitarians  :  whether  upon  the  evidence  of  this 
writing   only,    or   the  general   evidence,    does   not    precisely   appear : 


58  NEWTON 

not  merely  to  their  tenets,  but  to  each  and  every 
mode  of  maintaining  them.  And  writers  who  go 
so  far  as  to  say  anything  against  one  mode  of 
supporting  their  own  side  of  a  question,  generally 
make  a  decided  profession  of  adherence  to  the  con- 
clusion while  they  reason  against  one  mode  of 
maintaining  it.  Newton  does  no  such  thing  :  his 
expressions  are  vague,  or,  if  not  vague,  they  are  the 
formular  x  words  under  which  the  opponents  of  the 

probably  upon  the  former  alone.  The  author  of  the  Life  in  the 
Biographia  Britannica  does  not  mention  these  letters.  But  it  appears 
by  the  testimony  of  Le  Clerc  and  Wetstein,  that  Locke  sent  them  to 
Le  Clerc,  who  did  not  know  their  author.  The  possessors  of  Newton's 
papers  never  published  them  until  an  incomplete  edition  had  appeared 
abroad. 

1  Sir  D.  Brewster,  to  whom  the  admirers  of  Newton  have  much 
obligation,  and  from  whom  they  expect  more,  in  the  larger  Life  on 
which  he  is  known  to  be  engaged,  argues  from  these  words,  which  he 
quotes  formally,  that  Newton  received  the  Trinity.  But,  having  the  work 
before  him,  he  should  also  have  destroyed  the  effect  of  the  following  words 
of  Newton: — "  He  (Cyprian)  does  not  say  the  Father,  the  Word,  and 
the  Holy  Ghost,  as  it  is  now  in  the  7th  verse,  but  the  Father,  the  Son, 
and  the  Holy  Ghost,  as  it  is  in  Baptism,  the  place  from  ^vh^ch  they  tried 
at  first  to  derive  the  Trinity."  We  never  were  quite  satisfied  till  we 
saw  this  passage.  We  found  the  Trinitarian  writers  evidently  shy  of 
the  question :  and  the  Antitrinitarians  as  evidently  laying  such  an 
undue  stress  on  Mr  Haynes's  testimony,  or  rather  Mr  Baron's  testimony 
to  Mr  Haynes's  testimony,  as  made  us  suspect  that  our  authorities  on 
both  sides  were  not  fully  satisfied  in  their  own  minds.  But  we  hold  it 
to  be  out  of  the  question  that  a  Trinitarian  could  have  written  the 
words  in  our  italics.  That  many  would  riot  admit  the  baptismal  form 
in  itself  to  be  a  proof  of  the  doctrine,  is  known  ;  but  what  Trinitarian 
ever  talked  of  a  "  they"  who  tried  a  text  to  prove  the  doctrine,  "at 
first,"  implying  that  they  failed,  and  then  went  to  others?  the  clear 
implication  being  that  he  thought  they  had  the  doctrine  before  they 
tried  any  texts.  Again,  there  is  the  following.  Speaking  of  the 
manuscript  on  which  Erasmus  at  last  introduced  I  John  v.  7  into  his 
text,  he  says  that  the  English,  "  when  they  had  got  the  Trinity  into  his 
edition,  threw  by  their  manuscript  (if  they  had  one)  as  an  almanac  out 
of  date."  Now  most  of  our  readers  are  Trinitarians,  and  know  whether 
this  is  the  way  in  which  those  who  hold  that  doctrine  speak  of  it.  The 
citations  above  are  from  Horsley's  Newton. 

When  M.  Biot  said  that  there  was  absolutely  nothing  in  Newton's 
writings  which  was  other  than  orthodox,  he  must  have  meant  in  the 


NE  WTON  59 

received  doctrine  avoided  imprisonment.  The  truth 
is  to  be  purged  of  things  spurious  :  the  faith  sub- 
sisted before  these  texts  were  introduced  or  changed ; 
it  is  not  an  article  of  faith  or  a  point  of  discipline, 
but  a  criticism,  and  so  on.  There  is  an  expression 
towards  the  end  which  admits  of  a  double  interpre- 
tation :  ' '  if  the  ancient  churches,  in  debating  and 
deciding  the  greatest  mysteries  of  religion,  knew 
nothing  of  these  two  texts  ;  1  understand  not,  why 
we  should  be  so  fond  of  them  now  the  debates  are 
over."  The  first  clause,  by  itself,  might  rather 
have  been  written  by  a  Trinitarian :  though  a 
Unitarian  might  write  it,  more  especially  if  he 
wanted  a  formular  phrase.  But  the  second  clause 
looks  very  like  a  formula  :  for  there  was  no  time  at 
which  the  debate  raged  so  fiercely  as  in  the  day  of 
Newton,  which  was  that  of  Wallis,  South,  Sherlock, 
and  so  on,  and  hosts  of  anonymous  writers.  We 
find  it  difficult  to  suppose  that  Newton,  whose 
friendship  with  Locke,  Clarke,  and  Whiston  at 
that  time  was  notorious,  would  do  that  which  none 
but  Antitrinitarians,  or  very  few,  ever  did,  in  a 
communication  to  an  Antitrinitarian  intended  at 
that  time  for  publication  abroad,  without  making  a 
definite  avowal  of  the  orthodoxy  of  his  belief,  if  he 
had  it  to  make.  It  is  right  to  state,  on  the  other 

writings  which  he  had  seen.  This  of  course  may  have  been  the  case. 
Moreover,  what  is  more  absurd  than  to  argue  from  his  silence  that  a 
man  does  not  hold  an  opinion  for  which  he  might  be  ruined  and 
imprisoned,  or,  up  to  1699,  even  hanged?  [See  the  first  note  to  this 
Essay.] 


60  NEWTON 

side,  Bishop  Burgess's  argument :  that  this  was  a 
writing  which  Newton  suppressed  from  publication. 
Printing  should  have  been  the  word :  Newton 
published  it  when  he  caused  it  to  be  sent  to 
Le  Clerc.  There  is  to  us  something  corroborative, 
or  at  least  significative  of  much  difference  from  the 
most  common  opinion,  in  the  Scholium  which  he 
added  at  the  end  of  the  second  edition  of  the 
Principia.  With  Jewish  and  Christian  writers, 
Deity  is  necessarily  from  eternity  and  without 
superior :  the  word  God  implies  both  necessary 
existence  and  omnipotence.  With  the  Greeks, 
divine  power  might  be  communicated  in  such  a 
manner  that  a  hero,  for  instance,  after  death,  might 
become  as  truly  the  object  of  worship  as  Jupiter 
himself.  Newton  adopts  the  Greek  definition,  or 
one  very  like  it.  The  rule  of  a  spiritual  being 
makes  him  God.  "Dominatio  entis  spiritualis 
Deum  constituit."  And  as  if  this  were  not  precise 
enough,  he  adds,  in  the  third  edition,  a  note  stating 
that  thus  the  souls  of  dead  princes  were  called  gods 
by  the  Gentiles,  but  falsely ',  from  want  of  dominion. 
He  then  proceeds  to  his  well-known  reflections  on 
the  Supreme  Deity. 

We  have  entered  into  this  question,  not  from  any 
particular  interest  in  it — for  there  are  too  many 
great  minds  on  both  sides  of  the  controversy  to  make 
one  more  or  less  a  matter  of  any  consequence  to 
either, — but  because  we  have  a  curious  matter  of 


NEWTON  6 1 

evidence,  and  an  instructive  view  of  party  methods 
of  discussion.  Whatever  Newton's  opinions  were, 
they  were  in  the  highest  degree  the  result  of  a  love 
of  truth,  and  of  a  cautious  and  deliberate  search 
after  it.  His  very  infirmity  is  a  guarantee  for  the 
existence  of  this  feeling  in  no  usual  measure.  With 
a  competent  livelihood,  and  the  dread  of  discussion 
so  strong  that  he  would  gladly  have  hidden  his 
results  from  the  world  rather  than  encounter  even 
respectful  opposition,  he  could  not  have  worked  either 
for  the  hope  of  wealth  or  office,  or  even  for  the  love 
of  fame,  except  in  a  very  secondary  degree.  The 
enthusiasm  which  supported  him  through  the  years 
of  patient  thought  out  of  which  the  Principia  arose, 
must  have  been  strong  indeed  when  he  had  no 
ultimate  worldly  end  to  propose  to  himself.  Who 
can  say  how  much  of  the  truth  of  his  system  we  may 
owe  to  this  very  position  ?  Had  he  been  desirous 
of  pleasing,  he  must  have  had  strong  temptation 
to  build  upon  some  of  the  prevailing  notions  ;  to 
have  a  little  mercy  upon  the  physics  of  Descartes. 
Or  even  without  going  so  far,  a  small  portion  of  the 
vanity  which  loves  to  present  complete  systems  and 
to  confess  no  ignorance,  might  have  biased  him  to 
adopt  such  an  addition  to  his  law  of  attractive  force 
(such  a  one  as  Clairaut  for  a  little  while  thought 
necessary)  as,  without  interfering  with  the  main 
phenomena,  would  have  served  to  bring  out  some 
more  explanations.  But  he  had  no  such  bias  :  and 


62  NE  WTON 

speaking  of  his  philosophic  character,  it  may  be  said 
that  never  was  there  more  of  the  disinterested  spirit 
of  inquiry,  unspurred  by  love  of  system,  unchecked 
by  dread  of  labour  or  of  opinion.  For,  however 
much  he  might  dislike  or  fear  opposition,  there  was 
one  tribute  to  it  which  his  philosophy  never  paid  ; 
the  pages  which  he  would  gladly  have  burned  rather 
than  encounter  discussion,  contain  no  concession 
whatever. l 

XII 

In  concluding  this  brief  outline  of  a  truly  great 
man,  one  of  the  first  minds  of  any  age  or  country, 
of  whose  labours  the  world  will  reap  the  fruits  in 
every  year  of  its  existence,  we  cannot  help  express- 
ing our  hope  that  future  biographers  will  fairly 
refute,  or  fairly  admit,  the  existence  of  those  blots 
of  temper  to  which  the  undiscriminating  admiration 
of  preceding  ones  has  obliged  us  to  devote  so  much 
of  the  present  article.  Of  the  facts,  where  we  have 
stated  them  as  facts,  we  are  well  assured  ;  and  there 
can  be  no  reason  why  the  warnings  which  the  best 
and  greatest  of  the  species  must  sometimes  hold  out 
to  the  rest,  should  be  softened,  or,  what  is  worse, 
converted  into  examples  of  imitation,  by  fear  of 
opposing  an  established  prejudice,  or  by  the  curious 
tendency  of  biographers  to  exalt  those  of  whom 

1  [On  Newton's   religious   opinions,  see   also  §  VIII.  of  the   third 
Essay,  below.] 


NE  WTON  63 

they  write  into  monsters  of  perfection.  Surely  it  is 
enough  that  Newton  is  the  greatest  of  philosophers, 
and  one  of  the  best  of  men — that  all  his  errors  are 
to  be  traced  to  a  disposition  which  seems  to  have 
been  born l  with  him — that,  admitting  them  in  their 
fullest  extent,  he  remains  an  object  of  unqualified 
wonder,  and  all  but  unqualified  respect. 

For  reasons  which  will  be  easily  understood,  the 
author  of  this  article  subscribes  his  name. 

A.  DE  MORGAN. 

1  We  cannot  trace,  in  Newton's  character,  an  acquired  failing', 
nothing  but  the  manifestations  of  the  original  disposition  due  to 
different  circumstances. 


II 

A  SHORT  ACCOUNT  OF  SOME 

RECENT  DISCOVERIES  RELATIVE 

TO  THE  CONTROVERSY  ON  THE 

INVENTION  OF  FLUXIONS 


A  SHORT  ACCOUNT  OF  SOME 

RECENT  DISCOVERIES  IN  ENGLAND 

AND  GERMANY  RELATIVE  TO  THE 

CONTROVERSY  ON  THE  INVENTION 

OF  FLUXIONS1 

THE  celebrated  controversy  on  the  invention  of 
fluxions  has,  any  one  would  suppose,  been  so  fully 
argued  that  it  would  be  difficult  to  make  out  a 
reasonable  case  for  introducing  the  subject  again. 
It  is  nevertheless  true  that  several  disclosures  of 
great  importance  in  the  way  of  evidence  have  never 
been  made  at  all  until  very  lately. 

This  controversy  resembles  one  of  those  well-worn 
law  cases  which  must  be  cited  and  discussed  when- 
ever a  certain  question  arises.  Every  dispute  about 

1  [This  Essay  was  printed  in  The  Companion  to  the  Almanac:  or, 
Year-Book  of  General  Information  for  1852,  pp.  5-20,  which  was 
published  at  London  by  Charles  Knight  as  a  supplement  to  The  British 
Almanac  of  the  Society  for  the  Diffusion  of  Useful  Knowledge,  for  the 
year  of  our  Lord  1852,  and  of  which  the  first  part,  in  which  the  present 
Essay  was  included,  contained  "general  information  on  subjects  of 
mathematics,  natural  philosophy  and  history,  chronology,  geography, 
statistics,  etc."  It  seems  to  have  been  the  first  English  consideration 
of  the  fluxional  controversy  in  the  light  of  the  discoveries  of  Gerhardt 
among  Leibniz's  manuscripts  in  the  Royal  Library  of  Hanover.  Notes 
on  the  literature  relating  to  the  controversy,  and  on  the  early  fluxional 
manuscripts  of  Newton  and  Leibniz,  are  given  below  in  the  Appendix  to 
this  Essay.] 

67 


68  FLU XI  ON AL 

priority  of  mathematical  invention l  revives  it.  At 
the  same  time,  the  main  and  turning  points  of  it 
can  be  presented  without  any  such  amount  of 
mathematical  language  as  would  render  an  article 
upon  the  subject  unfit  for  the  majority  of  readers. 
We  therefore  propose  to  present  some  of  these 
points,  with  an  account  of  the  recently  published 
materials,  and  of  their  bearing  on  the  result. 

When,  after  some  petty  and  indecisive  controversy, 
Leibniz  appealed  (1711)  to  the  Royal  Society  for 
protection  against  imputations  of  plagiarism  which 
had  at  last  assumed  a  distinct  form,  the  Society,  in 
1712,  appointed  the  celebrated  partisan  2  Committee 
to  maintain  the  side  of  Newton.  The  report  of  this 
Committee,  published  with  epistolary  evidence  in 
1712,  under  the  name  of  Commercium  Epistolicum* 
contains  the  following  sentence,  which  is  the  whole 

1  One  most  fortunate  circumstance  about  it,  as  a  precedent,  is  that 
it  fixed  the  meaning  of  the  word  "publication"  to  the   genuine  and 
legal  sense.     It  is  the  sufficient  answer  to  any  one  who  would  restrict 
this  word  to  its  colloquial  sense  of  circulation  by  means  of  type. 

2  We  have  shown  the  Committee  to  have  had  this  character  in  Phil. 
Trans. ,  part  ii.  for  1 846,  and  in  the  life  of  Newton  in  Knighfs  British 
Worthies  ;   and   nobody   has  contested   the  point.     It  was,  however, 
universally  believed  that  the  intended  function  of  the  Committee  was 
judicial,  and  both  Newton  and  Leibniz  speak  of  it  as  if  it  had  been  so. 
But  though  the  Committee  itself  overstepped  its  own  proper  function  in 
the  form  of  its  decision,  and  thereby  gave  rise  to  the  misconception,  we 
hold  the  intention  of  its  proposers   to   have  been  stated  with  perfect 
clearness.     [On  De  Morgan's  paper  in  the  Philosophical  Transactions 
for  1846,  and  on  the  subsequent  occurrences,  see  the  above  Preface  to 
these  Essays  and  Appendix  ii.  to  the  third  Essay  below.  ] 

3  We  cannot  here   detail   all   the  circumstances.     The  reader  may 
consult  the  articles  "  Commercium  Epistolicum"  and  "Fluxions"  in 
the   Penny  Cyclopaedia^  the  life  of  Newton  already  cited,  Brewster's 
Life  of  Newton,  that  in  the  Library  of  Useful  Knowledge,  or  Weld's 
History  of  the  Royal  Society. 


CALCULUS  69 

of  that  report,  so  far  as  it  insinuates  that  Leibniz 
did  take,  or  might  have  taken,  his  method  from' 
that  of  Newton  : — "  And  we  find  no  mention  of  his 
(i.  e.  Leibniz's)  having  any  other  Differential  Method 
than  Moutoris  before  his  Letter  of  2ist  of  June 
1677,  which  was  a  Year  after  a  Copy  of  Mr  Newton's 
Letter,  of  loth  of  December  1672,  had  been  sent  to 
Paris  to  be  communicated  to  him  ;  and  about  four 
Years  after  Mr  Collins  began  to  communicate  that 
Letter  to  his  Correspondents  ;  in  which  Letter  the 
Method  of  Fluxions  was  sufficiently  describ'd  to  any 
intelligent  Person." 

The  Committee  in  their  English  have  "any  in- 
telligent person " ;  in  their  Latin,  subjoined  for 
foreigners,  they  have  '  ?  idoneo  harum  rerum  cog- 
nitori."  Raphson,  no  stickler  for  accurate  de- 
scription, as  we  shall  see,  could  not  second  this  ; 
so  he  converts  the  Latin  into  the  original,  and  gives 
his  own  English  translation,  * '  to  any  proper  judge 
of  these  matters."  But  even  this  was  too  much; 
so  some  one  else  (copied  by  Hutton  in  his  Dictionary  ; 
we  do  not  think  Hutton  did  it  himself)  has  invented 
a  new  report,  in  which  we  find  (<a  man  of  his 
sagacity." 

How  far  this  celebrated  letter  deserves  the  char- 
acter here  given  of  it,  is  one  question ;  whether 
Leibniz  actually  received  it,  is  another.  Compara- 
tively little  notice  was  taken  of  either ;  so  that  in 
many  subsequent  writings  it  reminds  us  of  the  tree 


70  FLUXIONAL 

which  was  cut  down  that  the  action  for  trespass 
might  try  the  ownership  of  the  estate.  It  gives, 
nevertheless,  the  only  possibility,  such  as  it  is, 
which  the  evidence  offers  of  Leibniz  having  seen 
anything  to  the  point  from  the  pen  of  Newton. 

In  order  to  prove  the  passage  quoted  above,  it 
is  stated  that  there  existed,  among  the  papers  of 
Collins  in  the  possession  of  the  Royal  Society,  in 
the  handwriting  of  Collins,  a  parcel  (collectid)  of 
papers  containing  extracts  from  Gregory's  letters, 
together  with  the  letter  of  Newton  above-mentioned 
(but  which  was  not  alluded  to  in  the  title  or  docket 
which  Collins  placed  on  the  parcel),  and  that  the 
parcel  was  marked  as  to  be  communicated  to 
Leibniz,  and  was  accompanied  by  a  copy  of  a  letter 
to  Oldenburg,  the  party  who  was  to  make  the 
communication.  Not  a  word  is  said  on  the  date 
at  which  the  parcel  was  transmitted  :  so  that  the 
Committee,  in  their  report,  actually  added  a  state- 
ment for  which  there  was  no  pretext  of  evidence, 
namely,  that  Newton's  letter  was  transmitted  about 
a  year  before  the  2ist  of  June,  1677.  Further,  the 
evidence  does  not  mention  the  date  at  which  Collins 
died  (1682),  nor  how  his  papers  came  into  the 
possession  of  the  Society,  nor  whether  there  was 
any  guarantee  that  papers  found  tied  together  in 
1712  had  been  so  tied  up  by  Collins  before  1682, 
nor  whether  there  was  any  evidence  that  Collins 
had  fulfilled  his  intention  of  sending  the  parcel  on 


CALCULUS  71 

to  Oldenburg,  and  so  on.  When  Leibniz,  who  did 
not  remember  receiving  any  such  letter,  declared 
that  he  did  not  think  it  necessary  to  answer  any- 
thing so  weak,  his  contempt  for  this  unattested 
statement  was  of  course  construed  by  the  other 
side  as  being  of  that  kind  which  parties  who  cannot 
answer  find  it  convenient  to  assume. 

The  editors,  whoever  they  were,  of  the  reprint l 
of  the  Commercium  Epistolicum,  made  under  the 
sanction  of  the  Royal  Society  in  1722,  took  the 
liberty  of  secretly  making  a  few  additions2  and 
alterations.  Among  these,  they  add  the  date  at 
which  Collins  died,  and  the  date  of  transmission  of 
the  parcel :  they  say  it  was  sent  on  June  the  26th, 
1676.  How  they  got  this  date  is  not  said  ;  but  as 
the  next  parcel  sent  by  Oldenburg  to  Leibniz  was 
stated  to  have  been  sent  on  June  the  26th,  it  may 
have  happened  that  the  revisers  of  the  second  edition 
borrowed  this  date  for  their  purpose. 

So  the  matter  rested  until  recently,  when  the 
publication  of  a  portion3  of  Leibniz's  papers  took 

1  We   say  "reprint,"  and  not  "second  edition,"  because  even  the 
old  title-pages  and  the  old   date   (1712)  were  reprinted.     Everything 
was  done  which  could  lead  the  reader  to  suppose  that  he  had  in  every 
respect  a  repetition  of  the  original  work,  preceded  by  a  preface  of  the 
new  editors. 

2  This  fact   was  discovered  by  us  in  1848  ;   and  the  additions  are 
exposed    in    the   Philosophical    Magazine   for  June    1848.       The   first 
edition  is  now  scarce.      [See  the  above  Preface  and  Appendix  ii.  to 
the  third  Essay.] 

3  Leibnizens  mathematische  Schriften,  herausgegeben  von  C,  J.    Ger- 
hardt,  Berlin,  8vo.     Erste  Abtheilung,  Band  I,  1849,  Band  II,  1850. 
We  have  not  seen  any   more,  if  indeed  any  more  has  yet  appeared. 
[Leibnizens  mathematische  Schriften  were  edited  by  C.  I.  Gerhardt  as 


72  FLUXION AL 

place.  And  it  now  appears  that  if  the  manuscripts 
which  Leibniz  left  behind  him,  and  which  found 
their  way  into  the  Royal  Library  at  Hanover,  had 
been  examined,  it  could  have  been  ascertained  what 
Leibniz  really  did  receive  from  Oldenburg.  It 
appears  that  the  latter  wrote  to  the  former  from 
London,  with  the  date  of  July  the  26th,  1676,  not 
forwarding  Collins's  parcel,  but  describing  its 
contents1  himself.  He  gives  various  matters  con- 
nected with  Gregory's  researches,  and  then  proceeds 
to  allude  to  a  method  in  a  letter  from  Newton  of 
December  the  loth,  1672.  But  though  he  gives, 
almost  verbatim,  what  we  may  call  the  descriptive 

the  third  series  (Dritte  Folge:  MathemaliK)  of  G.  H.  Pertz's  edition 
of  Leibnizens  gesammelte  Werke  aus  den  Handschriflen  der  Kbniglichen 
Bibliothek  zu  Hannover,  and  were  published  in  seven  volumes.  In  the 
first  division  (Abtheilung},  vol.  i  (Berlin,  1849)  contained  the  corre- 
spondence with  Oldenburg,  Collins,  Newton,  Galloys,  and  Vitale 
Giordano ;  vol.  ii  (Berlin,  1850)  contained  the  correspondence  with 
Huygens  and  de  1'Hopital ;  vol.  iii  (Halle,  1855)  contained  that 
with  Jacob,  Johann,  and  Nicolaus  Bernoulli;  and  vol.  iv  (Halle, 
1859)  that  with  Wallis,  Varignon,  Guido  Grandi,  Zendrini,  and 
Tschirnhaus.  The  second  division  consists  of  three  volumes  of 
Leibniz's  mathematical  writings,  published  and  unpublished.  How- 
ever, none  of  the  important  papers  written  by  Leibniz  when  discovering 
the  calculus,  which  were  published  by  Gerhardt  in  1848  and  1855  (see 
the  Appendix  to  this  Essay),  were  included  in  these  volumes.  Vol.  v 
(numbering  consecutively  to  the  others)  was  published  at  Halle  in  1858, 
and  contained  those  mathematical  writings  which  were  either  published 
(1666-1713)  or  intended  for  publication  ;  vol.  vi  (Halle,  1860)  con- 
tained writings  on  dynamics  from  1671  to  1706;  and  vol.  vii  (Halle, 
1863)  was  on  "  Initia  mathematica  ;  Mathesis  universalis  ;  Arithmetica ; 
Algebraica;"  and  "Geometrica."  Gerhardt  also  published  at  Berlin 
in  1899  the  Briefwechsel  mentioned  in  the  Appendix  to  this  Essay.] 

1  Collins  had  desired,  in  the  title  of  the  parcel,  that  the  contents 
after  being  read  by  Leibniz,  should  be  returned  to  himself.  Olden- 
burg appears  to  have  thought  it  more  prudent  to  write  his  own 
account  than  to  trust  the  papers  to  accident  by  land  and  sea,  (At 
least,  this  was  our  impression  before  we  came  to  the  discovery  presently 
mentioned. ) 


CALCULUS  73 

paragraph'*-  of  this  letter,  he  does  not  even  allude 
to  the  example  of  the  method,  in  which,  according 
to  the  report  of  the  Committee,  the  method  of 
fluxions  is  sufficiently  described  to  any  intelligent 
person.  So  that,  with  reference  to  this  asserted 
description  of  the  method  of  fluxions,  there  is  now 
clear  and  positive  evidence  that  Leibniz  did  not 
receive  it  as  stated,  but  received  only  an  account 
of  the  rest  of  the  letter,  which  describes  the  sort  of 
results  attainable. 

Towards  the  end  of  1850  the  Master  and  Fellows 
of  Trinity  College,  Cambridge,  published  (from 
among  their  manuscripts)2  the*  correspondence  of 

1  "  Defuncto    Gregorio,"    says    Oldenburg,    "  congressit    Collinius 
amplum  illud  commercium  litterarium,  quod  ipsi  inter  se  coluerant,  in 
quo  habetur  argumenti  hujus  de  seriebus  historia :  cui  Dn.  Newtonus 
pollicitus  est   se  adjecturum  suam  methodum  inventionis  illius,  prima 
quaque   occasione   commoda   edendam  ;   de  qua  interea  temporis  hoc 
scire  prseter  rem  non  fuerit,  quod  scilicet  Dn.  Newtonus  cum  in  literis 
suis  Dcbr.  10.  1672  communicaret  nobis  methodum  ducendi  tangentes 
ad  curvas  geometricas  ex  gequatione  experimente  relationem  ordinatarum 
ad  Basin,  subjicit  hoc   esse   unum  particulare,  vel  corollarium  potius, 
methodi  generalis,  quse  extendit  se  absque  molesto  calculo,  non  modo 
ad  ducendas  tangentes  accomodatas  omnibus  curvis,  sive  Geometricas 
sive  Mechanicas,  vel  quomodocunque  spectantes  lineas  rectas,  aliisve 
lineis   curvis ;   sic  etiam  ad  resolvenda   alia   abstrusiora   problematum 
genera  de  curvarum  flexu,  areis,  longitudinibus,  centris  gravitatis  etc. 
Neque   (sic  pergit)   ut   Huddenii   methodus   de   maximis   et  minimis, 
proinde  que  Slusii  nova  methodus  de  tangentibus  (ut  arbitror)  restricta 
est  ad  aequationes,  surdarum  quantitatum  immunes.     Hanc  methodum 
se  intertextuisse,  ait  Nowtonus  (sic),  alteri  illi,  quse  sequationes  expedit 
reducendo  eas  ad  infinitas  series ;   adjicit  que,  se  recordari,  aliquando 
data   occasione,    se   significasse  Doctori   Barrovio   lectiones  suas  jam 
edituro,  instructum  se  esse  tali  methodo  ducendi  tangentes,  sed  avoca- 
mentis  quibusdam  se  prsepeditum,  quominus  earn  ipsi  describeret." 

The  word  nobis •,  put  by  us  in  italics,  should  be  ei ;  Oldenburg  forgot 
that  he  was  describing,  not  copying,  the  account  Collins  had  given  him. 

2  Correspondence  of  Sir  Isaac  Newton  and  Professor  Cotes  .  .   .  now 
first  published  from   the  originals  in  the  Library  of  Trinity  College, 

Cambridge,   together  with   an  appendix  .  .  .  by  J.  Edleston,   M.A., 
Fellow  of  Trinity  College,  Cambridge,  London,  1850,  8vo. 


7  A  FLUXIONAL 

Newton  and  Cotes,  with  what  is  called  a  synoptical 
view  of  Newton's  life.  This  is  far  below  sufficient 
description  ;  for  the  synopsis  is  followed  by  a  body 
of  notes  of  such  research  and  digestion  as  make  it 
difficult  to  give  adequate  praise  to  the  whole  without 
appearance  of  exaggeration.  We  differ  much  from 
the  editor  as  to  many  matters  of  opinion  and  state- 
ments the  character  of  which  is  determined  by 
opinion  ;  and  we  take  particular  exception  to  the 
following  account 1  of  the  point  before  us  : — 

' '  Doubts  have  been  expressed  whether  these 
papers2  were  actually  sent  to  Leibniz.  We  have, 
however,  Collins's  own  testimony  that  they  were 
sent  as  had  been  desired,3  besides  Leibniz's  and 
Tschirnhaus's  acknowledgments  of  the  receipt  of 
them.4  It  may  also  be  observed  that  the  papers 
actually  sent  (in  a  letter  dated  July  the  26th,  1676) 
to  Leibniz  by  Oldenburg  have  been  recently  printed 
from  the  originals  in  the  Royal  Library  at  Hanover,5 
and  that  in  them,  as  in  Collins's  draught,  which  is 
preserved  at  the  Royal  Society  ('To  Leibnitz,  the 
1 4th  of  June,  1676  About  Mr.  Gregories  remains,' 
MSS.  Ixxxi.),  we  find  the  contents  of  Newton's 
letter  of  December  the  loth,  1672,  except  that 
instead  of  the  example  of  drawing  a  tangent  to  a 
curve,  there  is  merely  allusion  made  to  the  method. 

1  Op.  '«'/.,  p.  xlvii.  2  Comm.  Epist.,  p.  47  ;  2nd  ed.,  p.  128. 

3  Ibid.,  pp.  48  or  129  respectively. 

4  Ibid.,  pp.  58,  66  or  129,  142  respectively. 

5  Leibn.  Math.  Schrift.,  Berlin,  1849. 


CALCULUS  75 

Collins's  larger  paper  (called  '  Collectio  '  and  '  Hist- 
oriola '  in  the  Commercium  Epistolicum),  of  which 
the  paper  just  quoted  '  About  Mr.  Gregories  remains  ' 
is  an  abridgment,  and  which  contains  Newton's 
letter  of  December  the  loth  without  curtailment, 
is  stated  in  the  second  edition  of  the  Commercium 
to  have  been  sent  to  Leibniz,  but  whether  that  was 
the  case  may  be  fairly  questioned." 

There  are  two  things  in  which  we  have  never 
failed.  We  have  never  examined  a  point  of  mathe- 
matical history  without  finding  either  error  or 
difficulty  arising  from  bad  bibliography :  and  we 
have  never  come  fresh  to  this  controversy  of 
Newton  and  Leibniz  without  finding  new  evidence 
of  the  atrocious  unfairness  of  the  contemporary 
partisans  of  Newton.  Nor  had  we  a  perception, 
until  we  wrote  out  the  preceding  paragraph,  of  the 
full  extent  of  what  it  proves.  It  proves  that  at  the 
time  when  the  Committee  of  the  Royal  Society 
mentioned  the  ' '  collectio  "  which  contained  Newton's 
letter  uncurt ailed  of  any  part  relating  to  fluxions, 
and  asserted  in  their  final  report  (without  venturing 
to  mention  it  in  its  place)  that  this  letter  had  been 
forwarded  to  Leibniz — they  had,  and  must  have 
seen,  among  the  papers  they  were  appointed1  to 
examine,  Collins's  own  abridgment  of  this  "collectio," 
headed  "To  Leibnitz,"  and  containing  Newton's 

1  There  is  not  the  least  reason  to  suppose  that  any  papers  of  Collins's 
ever  came  into  the  possession  of  the  Royal  Society  after  the  Comm. 
Epist.  was  published. 


76  FLUXION AL 

letter  curtailed  of  the  very  part  of  which  they  asserted 
that  it  described  the  method  of  fluxions  sufficiently 
for  any  intelligent  person.  Of  this  abridgment  they 
make  no  mention.  We  now  see  why  the  statement 
that  the  ' '  collectio "  was  sent  to  Leibniz  was  not 
allowed  to  appear  in  its  place  ;  that  is,  when  the 
"collectio"  was  mentioned  in  the  body  of  the  work. 
Had  the  blot  been  hit,  they  would  have  pleaded 
some  mistake  or  forgetfulness,  would  have  produced 
the  abridgment,  and  would  have  taken  their  stand 
on  the  fragment  of  the  letter  descriptive  of  results. 
We  neither  believe,  nor  would  have  others  believe, 
that  in  the  proceeding  just  described  we  are 
necessarily  to  impute  guilty  unfairness  to  the  Com- 
mittee of  1712,  or  to  some  of  them  :  though  all  the 
circumstances  make  it  impossible  to  avoid  including 
this  hypothesis  among  the  probable  ones.  Inde- 
pendently of  our  knowledge  of  what  hero-worship 
can  lead  to,  even  in  our  own  day,  we  are  bound  to 
remember  that  all  the  notions  as  to  what  is  fair  and 
what  is  unfair  in  controversy,  have  undergone  much 
change  since  the  commencement  of  the  last  century. 
And  above  all,  the  idea  that  a  party  in  literary 
controversy  resembles  one  in  a  court  of  law,  who 
may,  with  certainty  of  allowance,  choose  his  own 
evidence,  suppress  what  does  not  suit,  and  mystify 
what  does,  is  now  much  less  in  force.  In  the 
particular  case  before  us,  perhaps  something  is  to 
be  allowed  for  hurry.  The  Committee  was  appointed 


CALCULUS  77 

in  parcels  on  March  the  6th,  2Oth,  27th,  and  April 
the  1 7th;  and  their  report  was  read  on  April  the 
24th.  But  the  hurry,  if  any,  was  their  own  fault. 
This  striking  fact,  that  the  very  papers  which  were 
examined  in  1712  prove  that  the  celebrated  letter 
was  not1  sent  to  Leibniz,  but  only  a  description 
(amounting  to  extract)  of  a  part  of  it,  and  that  part 
not  the  one  which  most  appears  to  sustain  the 
report  of  the  Committee,  throws  into  the  background 
the  remarks  which  we  intended  to  make  on  part  of 
the  paragraph  above  extracted  from  the  synoptical 
life  of  Newton.  These  must  now  be  mixed  up  with 
remarks  on  the  whole. 

The  editor  begins  by  stating  that  doubts  have 
been  thrown  on  the  question  whether  "  these  papers 
were  actually  sent  to  Leibniz."  By  these  papers, 
the  reference  tells  us  we  are  to  understand  the 
' '  collectio  "  which  has  been  spoken  of.  To  remove 
the  doubts  and  prove  that  *  *  these  papers "  were 
actually  sent,  we  are  first  referred  to  Collins's  own 
testimony.  The  reference  given  would  exclude 

1  It  is  now  clear  that  the  Royal  Society  owes  the  world  more  publica- 
tion from  its  archives  than  has  yet  taken  place  :  unfortunately,  it  is  not 
yet  alive  to  the  feeling  that  such  disclosures  as  those  of  the  surreptitious 
additions  to  the  reprint  of  the  Cotnm.  Episl.,  and  of  the  suppres- 
sion now  noted,  would  come  most  gracefully  from  itself.  It  is  on 
record  that  in  1716,  the  Abbe  Conti,  a  friend  of  both  parties,  spent 
some  hours  in  looking  over  the  letter  books  of  the  Royal  Society  to  see 
if  he  could  find  anything  omitted  in  the  Conitn.  Epist.  which  made 
either  for  Leibniz,  or  against  Newton  ;  and  that  he  found  nothing. 
But  it  now  appears  either  that  he  did  not  know  what  to  look  for,  or 
that  there  were  papers  which  did  not  come  in  his  way.  Be  it  one  or 
the  other,  the  credit  of  his  search  is  now  upset ;  and  Mr  Edleston's 
discovery  proves  that  another  is  wanted. 


78  FLUXIONAL 

Newton's  letter,  since  nothing  is  there  mentioned 
as  sent  to  Paris  except  either  Gregory's  writings, 
or  what  had  been  done  on  the  method  of  series  : 
the  drawing  of  tangents  to  curves  was  a  perfectly 
distinct  thing  in  the  language  of  the  day.  But  this 
reference  leads  us  to  a  proof  (though  one  is  not 
needed)  that  the  Committee  actually  saw  the 
abridgment  which  was  sent,  and  contrived  to  intro- 
duce reference  to  it  in  an  unintelligible  way  ;  so 
that  no  one  who  was  ignorant  of  the  existence  of 
the  abridgment  could  infer  that  anything  was  sent 
except  the  complete  * '  collectio. "  The  reference  is 
to  the  Commercium  Epistolicum^-  where  we  find  a 
letter  from  Collins  to  David  Gregory  (the  brother  of 
James,  whose  papers  were  in  question)  of  August  the 
nth,  1676,  in  which  Collins  says  that  he  had  put 
together  an  "  historiola "  of  the  writings  of  his 
brother  and  others,  in  about  twelve 2  sheets,  for 
preservation  in  the  archives  of  the  Society ;  and 
that  he  would  find  from  what  followed  the  letter 
(ex  sequentibus  comperies)  that  care  had  been  taken 
to  satisfy  the  wishes  of  the  French  mathematicians. 
Annexed  to  the  letter  is  a  memorandum  to  the 
effect  that  the  ' '  sequentia "  had  been  sent  both  to 
the  members  of  the  French  Academy,3  and  to 

1  Pp.  47,  48  ;  2nd  ed.,  p.  129. 

2  It  is  now,  Mr  Edleston  informs  us,  extant  in  thirteen  sheets  ;  from 
which  it  is  clear  that  this  "historiola,"  as  Collins  calls  it,  is  what  the 
Committee  called  the  ' '  collectio  "  ;  as  the  editor  notes. 

3  Among   these  was  Leibniz,  who,  as  we  learn  from  the   letter   of 
Collins   to   Oldenburg,  attached   to   the   "collectio,"  was  one  of  the 


CALCULUS  79 

David  Gregory.  Here,  then,  are  two  things  ;  the 
"  historiola "  mentioned  in  the  letter,  and  the 
"sequentia"  of  the  letter:  the  latter  was  sent  to 
Paris,  and  therefore  by  the  "  sequentia  "  we  are  to 
understand  Collins's  abridgment.  That  is  to  say, 
the  Committee,  which  extracted  as  much  from  Collins 
as  would  prove  that  something  was  sent,  did  not 
give  a  word  to  explain  what  was  sent :  and  inserted 
in  their  report  a  deliberate  statement  that  the  whole 
of  what  they  chose  to  call  the  fluxional  part  of 
Newton's  letter  had  been  sent. 

We  are  next  told  that  Leibniz 1  acknowledged  the 
receipt  of  ' '  these  papers  "  :  we  look  at  the  reference 
indicated,  and  we  find  that  Leibniz  does  (August  the 
2/th,  1676)  acknowledge  letters  of  July  the  26th, 


French  Academy  who  had  desired  to  have  an  account  of  Gregory's 
writings.  In  fact,  Leibniz  was  at  Paris  when  he  received  Oldenburg's 
account  of  Collins's  abridgment.  The  Committee,  who  say  that 
Newton's  letter  was  sent  to  Paris  to  be  communicated  to  him,  may 
seem  by  this  phrase  to  have  supposed  him  to  have  been  at  Hanover. 

1  Our  extract  says,  Leibniz  and  Tschirnhaus.  Now  though  the 
latter  did  write  from  Paris,  in  September,  acknowledging  something, 
yet  he  does  not  sufficiently  say  what,  and  even  the  Committee  have  put 
a  note  to  his  letter,  doubting,  from  its  internal  evidence,  whether  he 
could  have  seen  those  extracts  from  Gregory  which  were  sent  to  Leibniz. 
So  that  the  Committee  knew  nothing  positive  as  to  what  was  trans- 
mitted to  Tschirnhaus.  Moreover,  Tschirnhaus  was  not  Leibniz.  The 
whole  of  the  passage  on  which  this  note  is  written  struck  us  as  so 
singular,  so  contrary,  in  the  antagonism  of  its  two  portions,  to  the 
usual  clearness  of  the  whole  of  which  it  forms  a  part,  that  we  could 
not  help  suspecting  that  the  editor  had  been  misled  by  some  pre- 
decessor. And  at  last  we  found  out  by  whom.  Keill,  in  the  account 
of  the  ' '  Commercium  Epistolicum  "  published  in  English  in  the  Phil. 
Trans,  for  1715,  and  in  Latin  as  a  preface  to  the  reprint,  has  the  whole 
argument  with  the  affirmation  of  Collins  and  the  replies  of  Leibniz  and 
Tschirnhaus.  Keill  was  more  noted,  while  alive,  for  getting  his  friends 
into  embarrassments  than  for  his  discoveries  :  will  he  never  leave  off  his 
old  tricks  ? 


8o  FLU XI  ON AL 

which  the  editor  himself  immediately  proceeds  to 
inform  us,  both  from  the  Hanoverian  publication 
and  from  Collins's  draught,  did  not  contain  "  these 
papers,"  but  only  an  abridgment.  Finally,  the 
editor  concludes  that  it  may  be  "  fairly  questioned" 
whether  the  transmission  ever  took  place.  How 
can  this  be  ?  The  doubts  as  to  the  transmission,  he 
has  just  told  us,  are  removed  by  the  testimony  of 
Collins  the  transmitter  and  Leibniz  the  receiver. 
The  answer  is,  that  the  editor  himself  immediately 
proceeds  to  prove,  both  from  the  transmitter  and 
the  receiver,  that  what  was  transmitted  was  not  the 
"collectio"  of  the  Commercium  Epistolicuin,  but 
an  abridgment.  We  cannot  but  suppose  that  the 
editor  imagined  the  existence  of  the  abridgment  to 
be  known,  and  having  no  idea  that  he  himself  was 
the  first  to  draw  it  from  its  retirement,  considered 
the  "collectio"  and  its  abridgment  as  convertible 
documents,  and  the  information  they  conveyed  as 
substantially  the  same.  We,  however,  had  never 
found  a  trace,  in  any  writing  upon  the  subject,  of 
any  mention  of  the  smaller  document  ;  and  it  is 
clear  that  the  omission  of  the  example  of  Newton's 
method,  poor  as  the  pretext  against  Leibniz  would 
have  been  even  if  it  had  been  there,  destroys  the 
pretext 1  altogether. 

1  If  the  editor  meant  that  Newton's  letter  is  substantially  the  same 
as  to  the  real  information  it  could  give,  whether  with  or  without  the 
example  of  the  method  of  tangents,  we  not  only  agree  with  him  as  to 
the  fact,  but  should  have  agreed,  if  he  had  asserted  that  a  sheet  of 


CALCULUS  8 1 

We  shall  join  the  complete  elucidation  of  the  last 
assertion  with  the  establishment  of  another  state- 
ment of  Leibniz,  namely,  that  the  Committee  of  the 
Royal  Society  had  been  guilty  of  gross  suppression 
of  facts  unfavourable  to  themselves,  and  within 
their  own  knowledge.  We,  who  have  not  right  of 
access  to  the  archives  of  the  Society,  can  of  course 
only  further  show  this  (beyond  what  is  shown  by 
the  suppression  of  the  abridgment)  by  proving 
suppression  of  documents  which  had  been  already 
printed  ;  that  is,  by  showing  that  the  Committee 
either  entirely  suppressed  what  they  ought  to  have 
brought  forward,  or  contented  themselves  with 
reference  where  they  ought  to  have  produced 
extracts.  We  shall  confine  ourselves  to  what  is 
immediately  connected  with  the  unlucky  fragment  of 
Newton's  letter,  which  was  never  sent. 

First,  the  Committee  refer  to  the  method  which 
Sluse  had  given  for  drawing  tangents,1  and  which 
was  printed  in  the  Phil.  Trans,  as  early  as  1673. 
They  give  Oldenburg's  communication  to  Sluse  of 
Newton's  letter,  in  which  Sluse  learns  that  what  he 
had  communicated  was  already  known  to  Newton.2 
They  also  give  Newton's  admission 3  that  Sluse  not 


blank  paper  (after  what  Sluse  had  already  published)  would  have  done 
just  as  well.  But  our  reader  must  remember  that  it  is  not  the  rational 
interpretation  of  the  letter  which  is  the  matter  in  discussion,  but  the 
interpretation  of  the  Royal  Society's  Committee. 

1  Comm.    Epist.,   p.    106 ;    we   quote   the   second  edition   as   more 
accessible  than  the  first. 

2  Ibid.,  p.  1 06.  3  Ibid.,  p.  107. 

6 


82  FLU  XI  ON AL 

only  had  probably  an  actual  priority  of  discovery, 
but  that,  whether  or  no,  he  was  the  first  promulgator. 
All  this,  so  far  as  it  goes,  is  fair,  though  it  militates 
strongly  against  the  conclusion  of  their  report  with 
respect  to  Leibniz.  But  it  was  not  fair  to  suppress 
all  account  of  the  manner  in  which  this  celebrated 
letter  of  Newton  was  drawn  out.  When  they  state 
that  Collins  had  been  for  four  years  circulating  the 
letter  in  which  the  method  of  fluxions  was  sufficiently 
described  to  any  intelligent  person,  they  suppress 
two  facts  :  first,  that  the  letter  itself  was  in  con- 
sequence of  Newton's  learning  that  Sluse  had  a 
method  of  tangents  ;  secondly,  that  it  revealed  no 
more  than  Sluse  had  done.  In  the  third  volume 
(1699)  of  Wallis's  works1  is  a  fragment  of  a  letter 
from  Collins  to  Newton,  of  June  the  i8th,  1673,  m 
which  he  reminds  Newton,  for  what  purpose  does 
not  appear,  of  his  having  communicated  the  fact  of 
Sluse's  discovery,  and  having  received  an  answer 
(which  was  no  doubt  the  letter)  for  the  purpose  of 
transmission  to  Sluse.  Again,  this  method  of  Sluse 
is  never  allowed  to  appear ;  reference  is  made  to 
the  Philosophical  Transactions,  though  many  things 
which  had  been  printed  before  appear  in  the  Com- 
mercium  Epistolicum  when  they  serve  the  right 
purpose. 

To  show  what  we  assert  we  shall   compare   the 
two  methods. 

1  In  Latin  p.  617,  in  English  p.  636. 


CALCULUS  83 

The  paragraph  of  Newton's  letter,  from  the 
original  in  the  Macclesfield  collection,  is  as  follows 
(December  the  loth,  1672): — 

"  I  am  heartily  glad  at  the  acceptance,  which  our 
rev.  friend  Dr.  Barrow's  Lectures  find  with  foreign 
mathematicians,  and  it  pleased  me  not  a  little  to 
understand  that  they l  are  fallen  into  the  same 
method  of  drawing  tangents  with  me  (eandem  .  .  . 
ducendi  tangentes  methodum).  What  I  guess  their 
method  to  be  you  will  apprehend  by  this  example. 
Suppose  CB,  applied  to  AB  in  any  given  angle,  be 
terminated  at  any  curved  line  AC,  and  calling  AB  x 
and  BC 'y,  let  the  relation  between  x  and  y  be  ex- 
pressed by  any  equation  as 

^3  _  2x*y  4.  bx*  -  b*x  +  by*  —y*  =  o, 

whereby  this  curve  is  determined.  To  draw  the 
tangent  CD,  the  rule  is  this.  Multiply  the  terms  of 
the  equation  by  any  arithmetical  progression  accord- 
ing to  the  dimensions  of  yt  suppose  thus 

x*  -  2x*y  +  bx*  -  b*x+  by*  -y*  . 
01         0023* 

also  according  to  the  dimensions  of  xy  suppose  thus 

x*  -  2x*y  +  bx*  -  b*x+  by*  -y* . 
32         2        100 

1  There  is  no  end  of  the  curiosities  of  this  Committee.  After  their 
Latin  for  the  word  "they,"  they  inserted  in  brackets  (Sluse  and 
Gregory),  the  latter  not  being  a  foreigner.  If  they  had  given  the 
letter  of  Collins,  just  referred  to,  of  June  the  i8th,  1673,  the  reader 
would  have  known  that  Sluse  and  Ricci  are  the  parties  understood. 


84  FLU XI  ON AL 

The  first  product  shall  be  the  numerator,  and  the 
last  divided  by  x  the  denominator  of  a  fraction,  which 
expresseth  the  length  of  BDy  to  whose  end  D  the 
tangent  CD  must  be  drawn.  The  length. of  BD 
therefore  is 

—  2xLy  +  2byL  —  3?>3  divided  by  3*2  —  <\xy  +  2bx  -  b\  " 

Not  many  days  afterwards  (January  the  I7th, 
X673)  Sluse  wrote  an  account  of  the  method  which 
he  had  previously  signified  to  Collins,  for  the  Royal 
Society,  by  whom  it  was  printed.1  The  rule  is  pre- 
cisely that  of  Newton,  the  exponents  are  multipliers, 
without  any  subsequent  reduction  of  the  exponents 
(which  prevents  both  explanations  2  from  describing 
the  method  of  fluxions  to  any  intelligent  person), 
and  instead  of  dividing  by  x,  Sluse  changes  one  x 
into  BDy  and  then  equates  the  two  results.  To 
have  given  this  would  have  shown  the  world  that 
the  grand  communication  which  was  asserted  to 
have  been  sent  to  Leibniz  in  June  1676  might  have 
been  seen  in  print,  and  learned  from  Sluse,  at  any 
time  in  several  previous  years  :  accordingly,  it  was 
buried  under  a  reference.  But,  worse  than  this,  the 
Committee  had  evidence  before  them  that  it  had  been 

1  Phil.  Trans.,  No.  90 ;  also  Lowthorp,  vol.  i,  pp.  18-20.     [J.  Low- 
thorp  abridged  the  Philosophical  Transactions  to  the  end  of  1706  into 
three  volumes.] 

2  If  Newton's  example  had  been  sent  to  Leibniz,  and  the  latter  had 
not  known  the  method  already  from  Sluse,  the  direction  to  multiply  by 
the  terms  of  any  arithmetical  progression  (a  mere  slip  of  the  pen  on 
Newton's  part,  properly  preserved  by  the  Latin  translator)  might  have 
puzzled  any  "  idoneus  harum  rerum  cognitor. '' 


CALCULUS  85 

so  seen  by  Leibniz,  and  this  evidence  they  deliberately 
mutilated. 

On  March  the  5th,  1677,  Collins  wrote  to  Newton, 
giving  him  certain  extracts  from  a  letter  of  Leibniz, 
dated  November  the  i8th,  1676.  This  was  printed 
(1699)  in  the  third  volume  of  Wallis.  Leibniz  had 
seen  Hudde  at  Amsterdam,  and  had  found  that 
Hudde  was  in  possession  of  even  more  than  Sluse  ; 
and  this  he  states,  referring  to  the  published  method 
of  Sluse,  as  known  to  himself.  He  gives  also  an 
example,  or  rather  its  result,  not  as  showing  the 
method,  which  was  known,  but  in  order  further  to 
show  how  to  eliminate  one  of  the  co-ordinates  from 
the  result.  The  Committee  omit  this  example,  with- 
out any  notice  of  omission,  though  they  give  the 
passages  between  which  it  lies. 

We  are  obliged  frequently  to  recur  to  the  assertion 
of  the  Committee  that  Newton's  example,  which  we 
have  translated,  was  description  enough  of  the  method 
of  fluxions  for  any  intelligent  person.  That  this, 
which  we  shall  believe  to  be  the  most  reckless 
assertion  ever  made  on  a  mathematical  subject,  until 
some  one  produces  its  match,  was  solemnly  put 
forward  by  the  Committee,  is  not  in  our  day  excuse 
enough  for  dwelling  upon  it.  But  the  sufficient 
excuse  is  that  writers  of  note,  upon  the  Newtonian 
side  of  the  question,  still  quote  the  assertion  with 
approbation.  In  Sir  David  Brewster's  Life  of  Newton, 
for  instance,  the  whole  Report  of  the  Committee  is 


86  FLUXIONAL 

printed,  and  a  virtual  adhesion  given  to  it.  On  the 
other  hand,  the  defenders  of  Leibniz,  most  of  whom 
are  not  English,  prefer  to  establish  his  rights  inde- 
pendently, and  evade  an  encounter  which  is  rendered 
repulsive  by  its  dealing  more  with  the  comparison  of 
old  letters  than  with  mathematical  explanations. 

Some  little  question  has  arisen  as  to  the  position 
in  which  the  Royal  Society  stands  in  this  matter. 
According  to  Leibniz,  Chamberlayne  wrote  to  him 
to  the  effect  that  the  Royal  Society  did  not  wish  the 
report  to  pass  for  a  decision  of  its  own.  Mr  Weld  l 
found  the  minute  in  question  (passed  May  the  2oth, 
1714),  in  which  it  is  stated  that  "if  any  person  had 
any  material  objection  against  the  Commercium^  or 
the  Report  of  the  Committee,  it  might  be  recon- 
sidered at  any  time."  This  Mr  Weld  considers  as 
an  adoption  of  the  Report  of  the  Committee  :  in 
which  we  cannot  join,  though  we  admit  that  it  throws 
the  question  open,  which  as  long  as  Chamberlayne's 
communication  stood  unanswered,  was  settled  :  and 
enables  us  to  infer  adoption  from  previous  acts.  In 
all  probability  he  informed  Leibniz  that  the  Report 
of  the  Committee  was  not  to  pass  for  a  decision, 
meaning  the  stress  to  lie  there,  and  stating  why  : 
and  this  would  be  correct,  for  a  question  which  may 
be  reconsidered  at  any  time  is  not  decided,  except 
in  a  technical  sense.  And  very  likely  he  added  * c  of 
the  Society  "  :  for  it  was  the  full  impression  of  the 

1  Phil.  Mag.,  1847  5  Hist.  Roy.  Soc.t  vol.  i,  p.  415, 


CALCULUS  87 

time  that  the  Society  was  one  with  its  Committee. 
There  can  be  no  doubt  that  the  hearty  adherence 
given  by  the  Society  to  the  conclusions,  the  circula- 
tion of  the  Commercium  Epistolicum  throughout 
Europe,  the  admission  of  Keill's  "  recensio  "  into  the 
Transactions,  the  sanction  of  the  reprint  ten  years 
after,  and  the  obstinate  determination,  which  lasts 
down  to  our  own  time,  not  to  confess  one  atom  of 
the  error  nor  right  one  atom  of  the  wrong,  amount 
to  an  adoption  which  could  not  be  more  than  ade- 
quately represented  by  any  quantity  of  minutes. 

It  seems  the  fate  of  this  controversy  that  whatever 
the  English  partisans  of  the  eighteenth  century 
supposed  to  have  happened  between  the  two  parties 
really  happened  the  other  way,  the  places  of  the 
parties  being  changed,  and  to  no  effect  upon  the 
question.  Much  stress  was  laid  on  Collins  trans- 
mitting from  Newton  to  Leibniz  an  example  of  the 
method  of  tangents  :  it  appears  that  the  example 
was  not  sent,  that  the  abridgment  sent  did  not  con- 
tain it  ;  but  it  appears  that  Collins  really  forwarded 
a  result  from  Leibniz  to  Newton,  which  was  the  only 
one  that  passed  between  them.  Not  that  this  gave 
Newton  any  information  ;  but  neither  would  Newton's 
example,  if  sent,  have  given  any  to  Leibniz,  after 
Sluse's  publication  and  Hudde's  oral  communication. 
Again,  it  was  frequently  stated  that  the  differential 
calculus  was  only  the  method  of  fluxions  with  the 
notation  changed.  Now  the  fact  is,  that  as  to  every- 


88  FLUXION AL 

thing  elementary  that  was  published  with  demonstra- 
tion under  the  name  of  fluxions ,  up  to  the  year  1704 
(when  Newton  himself  first  published  anything  under 
that  name)  the  method  of  fluxions  was  nothing  but 
the  differential  calculus  with  the  notation  changed. 
We  know  that  Newtek's  letters  did  not  treat  of 
fluxions,  nor  contain  anything  from  which  the  writer 
of  a  system  could  draw  his  materials.  No  one 
ventured  to  print  an  elementary  treatise  in  England 
until  the  seed  had  grown  into  a  strong  plant  under 
the  care  of  Leibniz,  the  Bernoullis,  and  so  on.  When 
de  1'Hopital,  in  1696,  published  at  Paris  a  treatise  so 
systematic,  and  so  much  resembling  one  of  modern 
times,  that  it  might  be  used  even  now,  he  could  find 
nothing  English  to  quote,  except  a  slight  treatise 
of  Craig  on  quadratures,  published  in  1693.  He 
mentions  all  that  he  could  of  Newton,  and  even  says 
of  the  Principia  that  it  was  full  of  the  calculus ',  which 
is  not  true  ;  he  should  have  said  it  was  full x  of  the 
principles  on  which  the  calculus  is  founded,  and  of 
application  of  them  in  which  the  reader  (whatever 
might  have  been  the  case  with  the  author)  is  directed 
by  thought  without  calculus.  But  the  distinction  is 
one  which  was  not  then  appreciated  :  in  fact  it  needed 
the  calculus,  such  as  it  became,  to  show  it.  It  must 
be  remembered  that,  when  de  1'Hopital  wrote  (for 

1  "C'est  encore  une  justice  due  au  scavant  M.  Newton,  et  que  M. 
Leibnis  luy  a  rendue  luy-meme :  Qu'il  avoit  aussi  trouve  quelque 
chose  de  semblable  au  calcul  dififerentiel,  comme  il  paroit  par  1'excellent 
Livre  intitule  .  .  .  Principia  .  .  .  lequel  est  presque  tout  de  ce  calcul." 
— Preface. 


CALCULUS  89 

he  could  then  have  seen  the  first  volume  of  Wallis), 
there  neither  was,  nor  had  been,  one  word  of  accusa- 
tion or  of  national  reflection,  to  create  any  bias  for 
or  against  any  one.      The  first  thing  of  this  kind  took 
place  in   1695,   when  Wallis,   in   the  preface  to  the 
first  volume  of  his  collected  works,  not  only  claimed 
the  differential  calculus  as  derived  from  the  method 
of  fluxions,  but  (in  ignorance,  as  he  afterwards  knew) 
grounded  the  claim  upon  the  two  celebrated  letters 
of'  Newton  to  Oldenburg,   of  which  little  notice  is 
taken  here,  because  not  even  the  Committee  of  the 
Royal  Society  venture  a  mention  of  them  in  their 
report,  as  any  ground  of  tonfirmation  against  Leibniz. 
The  note  of  alarm  thus  sounded,  our  countrymen 
began    to  write  upon  fluxions.      Some  writings  are 
so    advanced  that  they  do  not  define  their    terms  : 
from  these  therefore  we  cannot  tell  whether  x  means 
the  velocity  with  which  x  changes,   or  an  infinitely 
small  increment  of  x.     Such  (at  least  so  we  suppose 
from  the  enlarged  second  edition  of  1718)  was  the 
little  tract  of  Craig,  to  which  de  PHopital  refers,  as 
we  have  seen  :  and  such  were  Dr  Cheyne's  tract  on 
fluents  (1703)  and  De  Moivre's  answer  to  it  (1704). 
Newton  himself,  in  the  Principia,  was  not  a  fluxionist, 
but  a   differentialist.      Though    imagining    quantity 
generated  by  motion  or  flux  (in  the  celebrated  Lemma 
in  which  he  gives  a  brief  description),  he  calculates, 
not  by  velocities  but  by  moments,  or  "  momentaneous 
increments    and    decrements,"   which   are    infinitely 


90  FLUX  ION AL 

small  quantities,  for  "moments,  so  soon  as  they 
become  finite  magnitudes,  cease  to  be  moments." 
Of  Wallis  we  shall  presently  speak.  De  Moivre1 
represents  fluxions  as  momentaneous  increments  or 
decrements.  And  the  only  elementary  writers, 
Harris2  and  Hayes,3  are  strictly  writers  on  the 
differential  calculus,  as  opposed  to  fluxions,  in  every 
thing  but  using  x  instead  of  dx.  Harris  says,  "  By 
the  Doctrine  of  Fluxions  we  are  to  understand  the 
Arithmetick  of  the  Infinitely  small  Increments  or 
Decrements  ..."  These,  he  says,  Newton  pro- 
perly calls  fluxions ;  and  he  proceeds  to  show 
that  his  own  ideas  are  not  very  clear,  by  asserting 
that  "'Tis  much  more  natural  to  conceive  the 
Infinitely  small  Increments  or  Decrements  of  the 
variable  and  Flowing  Quantities,  under  the  notion 
of  Fluxions  (that  is,  according  to  him,  of  infinitely 
small  increments  or  decrements)  than  under  that  of 
Moments  or  Infinitely  small  Differences,  as  Leibnitz 
.  .  .  chose  rather  to  take  them."  And  then  he 

1  Phil.  Trans.,  1695,  No.  216. 

2  The   first  elementary  work   on  fluxions  in   England  is  a  tract  of 
twenty-two  pages  in  A  New  short  treatise  of  Algebra.  .  .  .   Together 
with  a  specimen  of  the  Nature  and  Algorithm  of  Fluxions.     By  John 
Harris,  M.A.,  London,  1702,  octavo  (small). 

3  A     Treatise   of  fluxions ;   or  an   Introduction   to    Mathematical 
Philosophy.      Containing  a  full  Explication  of  that  Method  by  which 
the  Most  Celebrated  Geometers  of  the  present  Age  have  made  such  vast 
Advances  in  Mechanical  Philosophy.     A    Work  very  Useful  for  those 
that  would  know  how  to  apply  Mathematicks  to  Nature.     By  Charles 
Hayes,  Gent.,  London,  folio,   1704.     This  work,  which  has  had  very 
little   notice  (Hayes,  born  1678,  died  1760,  wrote   many  works,  but 
never  set  his  name  to  any  but  this),  is  a  very  full  treatise,  nearly  three 
times  as  large  as  that  of  de  1'Hopital,  having  315  closely  printed  folio 
pages  on  fluxions,  besides  an  introduction  on  conic  sections. 


CALCULUS  91 

proceeds  to  speak  of  velocities  :  in  fact  he  jumbles 
de  PHopital,  whom  he  did  understand,  with  Wallis, 
whom  he  did  not.  Hayes,  a  much  clearer  writer, 
begins  thus:  "Magnitude  is  divisible  in  infinitum 
.  .  .  the  infinitely  little  Increment  or  Decrement 
is  called  the  Fluxion  of  that  Magnitude.  .  .  . 
Now  those  infinitely  little  Parts  being  extended,  are 
again  infinitely  Divisible  ;  and  these  infinitely  little 
Parts  of  an  Infinitely  little  Part  of  a  given  Quantity, 
are  by  Geometers  called  Infinitesimce  Infinitesi- 
marum  or  Fluxions  of  Fluxions. "  And  again * 
".  .  .  suppose  half  the  infinitely  little  increment 
of  X  to  be  \  x,  and  half  the  Fluxion  or  infinitely 
little  Increment  of  Z  to  be  \  z."  And  thus  it 
appears  that  all  explanation  that  was  tendered  in 
print,  up  to  the  year  1704,  whether  by  Newton  him- 
self, or  by  any  of  his  followers  (except  only  Wallis, 
as  presently  mentioned),  was  Leibnitian  in  principle. 
But  when  Newton,  in  1704,  published  the  treatise 
on  the  Quadrature  of  Curves  which  he  had  written 
before  Leibniz  communicated  the  differential  cal- 
culus to  him,  he  starts  with  nothing  but  the  notion 
of  quantity  increasing  or  diminishing  with  velocity, 
and  this  velocity  or  celerity  is  the  fluxion.  And  in 
the  Introduction,  written  at  the  time  of  publication, 
he  says,  "  I  do  not  consider  mathematical  quantities 
as  consisting  of  the  smallest  possible  parts  (paries 
quam  minima)  but  as  described  by  continuous 
1  ibid,,  p.  5. 


92  FLU  XI  ON AL 

motion."  This  is  the  first  public  declaration  of  the 
meaning  of  a  "  fluxion  "  that  was  made  by  the  author 
of  the  word,  in  his  own  name. 

It  may  appear  strange  that  we  defer  till  now  to 
mention  a  very  fluxional  view  of  fluxions  which 
appeared  as  early  as  1693.  But  we  wish  to  give  pro- 
minence to  what  is  really  Newton's  first  publication 
on  the  subject,  though  it  has  received  but  little  notice 
until  lately.  The  second  volume  of  Wallis's  works, 
containing  the  Algebra,  in  which  the  matter  spoken 
of  occurs,  was  published  in  1693,  the  first  in  1695, 
but  false  title-pages1  make  them  appear  as  of  1699. 
Again,  those  who  look  at  the  preface  to  the  first 
volume  see  that  Wallis  excuses  himself  from  men- 
tioning the  differential  calculus,  because  it  was 
nothing  but  the  fluxions  which  Newton,  he  says, 
had  communicated  to  Leibniz  in  the  celebrated 
Oldenburg  letters,  and  which  he  (Wallis)  had  de- 
scribed, from  those  letters,  nearly  word  for  word,  in 
his  Algebra.  No  one  of  later  times  would  thereupon 
refer  to  this  Algebra  for  information  ;  since  they 
would  know  that  nothing  upon  fluxions  could  be 
given  word  for  word,  but  only  letter  for  letter.  For 
all  that  is  said  upon  fluxions,  in  those  celebrated 

1  The  Comrn.  Epist,  says  that  two  volumes  appeared  in  1695  5  prob- 
ably the  second  volume  got  a  new  title-page  in  that  year.  The  third 
volume  was  published  in  1699,  and  then  the  first  volume  certainly  got 
a  title-page  of  that  date.  This  vile  practice  of  altering  title-pages  will 
be  put  down  by  the  scorn  of  all  honest  men,  so  soon  as  its  tendencies 
are  seen.  A  person  who  reads  Wallis's  collected  works  under  the  date 
of  1699  easily  convicts  the  author,  as  honest  a  man  as  ever  lived,  of 
the  grossest  unfairness,  upon  his  own  testimony. 

. 


CALCULUS  93 

epistles,  is,  as  is  well  known,  in  two  anagrams,  one 
of  which  is 

6a  2c  d  ae  136  2f  f\  3!  gn  40  4q  2r  45  Qt  I2v  x, 

the  information  given  being  that  whoever  can  form 
a  certain  sentence  properly  out  of  six  a's,  two  c's,  a 
</,  and  so  on,  will  see  as  much  as  one  sentence  can 
show  about  Newton's  mode  of  proceeding.  No  one 
but  Raphson1  imagined  that  any  human  being 
derived  any  information  from  this ;  and  probably 
therefore  few  would  be  induced  by  Wallis's  preface 
to  consult  the  work.  They  would  not  know  (and 
we  shall  see  that  Wallis  himself  could  hardly  have 
anything  to  make  him  remember)  that  Wallis  had 
been  in  communication  with  Newton,  had  obtained 
not  only  the  key  of  the  anagrams  but  their  meaning, 
and  had  added  a  brief  account  of  fluxions,  with  an 
extract  from  what  Newton  afterwards  published  in 
the  treatise  of  1704,  besides  other  matter  expressly 
obtained  from  Newton  in  explanation  of  the  second 

1  The  sentence  was  "  Data  yEquatione  quotcunque,  fluentes  quanti- 
tates  involvente,  fluxiones  invenire,  et  vice  versa,"  given  any  equation 
involving  fluent  quantities,  to  find  the  fluxions,  and  vice  versa.  Many 
writers  have  called  this  a  cipher •,  which  it  is  not :  a  cipher  gives,  in  some 
way,  the  order  of  the  letters  as  well  as  substitutes  for  the  letters  them- 
selves. Raphson  declared  that  Leibniz  had  first  deciphered  the  anagram, 
and  then  detected  the  meaning  of  the  word  fluxion,  after  which  he 
forged  a  resemblance.  But  Raphson  was  the  unscrupulous  man  of  the 
time,  if  any  one  could  deserve  that  name.  Newton  stated  distinctly 
that  Leibniz  sent  him  the  details  of  a  Method  which  was  his  own  in  all 
respects  except  language.  Raphson  says  (Hist,  of  Fluxions,  p.  I )  that 
Leibniz  "  writ  in  answer  that  he  had  found  out  a  Method  not  unlike  it, 
as  Sir  Isaac  himself  had  hinted,  page  253,  Princip.  ..."  The  im- 
pudence of  this  paraphrase  is  one  of  the  minor  gems  of  the  controversy  : 
and  we  could  rub  it  brighter  if  we  had  room. 


94  FLU XI  ON AL 

anagram.  The  reader  cannot  detect  the  new  infor- 
mation, except  in  that  additional  part  which  explains 
the  second  anagram  :  all  that  can  be  said  of  the  rest 
is,  that  to  a  reader  who  compares  chapters  91  and 

95  there  are  a    couple    of   sentences    which    would 
perhaps  puzzle  a  person  who  did  not  know  that  a 
new  source  of  information  was  referred  to  in  these 
sentences.      The    reviewer   of  Wallis    in    the    Acta 
Eruditorum,   in    complaining  of  the  suppression  of 
the  differential  calculus,  hit  the  real  reason,  namely, 
Wallis's  ignorance  of  a  good  deal  of  what  had  been 
done  abroad  :  and  Wallis,  who  wrote  to  Leibniz  the 
day  after  he  saw  this  review,  acknowledges  that  he 
knew  nothing  of  what  Leibniz  had  written,  except 
two  slight  and  old  papers,  and  had  never  heard  the 
name  of  the  differential l ,  calculus  until  the  preface 
was    in    the    press,   when    a  friend  mentioned  with 
indignation  that  Newton's  fluxions  were  current  in 
Belgium    under    that    name.      Then,    and    probably 
without    consulting    what    he    had    written,    Wallis 
added  the  sentence  we  have  mentioned  to  his  pre- 
face.     In  the  third    volume,   Wallis  printed  all  his 
correspondence  with  Leibniz,  and  all  the  correspond- 
ence   with    others    on    the    subject   which  he  could 

1  Nevertheless,  Leibniz  and  the  differential  method  are  mentioned  in 
the  second  volume,  that  is,  in  the  account  of  fluxions  on  which  we  are 
writing ;  but  (as  discovered  by  Professor  Rigaud)  Wallis's  copy  pre- 
served in  the  Savilian  Library  has  manuscript  additions  which  note 
and  explain  this  forgetfulness.  It  appears  that  the  whole  communica- 
tion is  Newton's,  and  is  inserted  in  Newton's  words  :  an  author  can 
hardly  remember  another  person's  writing,  to  which  he  gives  admission, 
as  if  it  were  his  own. 


CALCULUS  95 

collect,  and  mentions  fluxions  and  the  differential 
calculus  as  two  distinct  things  in  the  preface.  What 
we  have  here  to  do  with,  however,  is  the  nature  of 
the  publication  of  fluxions  which  was  made  in  1693. 
We  now  come  to  the  independent  proofs  of  the 
separate  invention  of  Leibniz,  as  contained  in  his 
recently  published  papers.  Preliminary,  however, 
to  these,  we  may  notice  one  which  was  published 
in  1671,  and  which  shows  the  way  in  which  the 
current  of  his  ideas  was  setting.  Dr  Hales,  in  his 
Analysis  Fluxionum^  says  that  Leibniz  had  given 
no  obscure  germs  of  his  differential  method  in  his 
Theoria  Notionum  Abstractarum^  dedicated  to  the 
French  Academy  in  1671  :  and  Dr  Hutton2  refers 
to  this  theory  of  abstract  notions.  Both  are  wrong 
in  the  name  ;  for  the  paper  which  Leibniz  dedicated 
to  the  Academy  in  that  year  is  Theoria  Motus 
Abstradi^  This  paper  is  certainly  a  witness  to 
character  ;  throughout  it  there  occurs  a  frequent  ap- 
proximation to  the  idea  of  infinitely  small  quantities 
having  ratio  to  each  other,  but  not  to  finite  quantities. 
One  extract  (translated)  will  serve  as  a  specimen  : 
"A  point  is  not  that  which  has  no  parts,  nor  of 
which  part  is  not  considered ;  but  which  has  no 
extension,  or  whose  parts  are  indistant,  whose 
magnitude  is  inconsiderable,  inassignable,  less  than 
any  which  has  ratio  (except  an  infinitely  small  one) 

1  London,  1800,  4to.  2  Math.  Diet.,  Art.  "Fluxions." 

3  Op.  Leibn.,  vol.  ii,  part  ii,  p.  35. 


96  FLUXIONAL 

to  a  sensible  quantity,  less  than  can  be  given  ;  and 
this  is  the  foundation  of  Cavalieri's  method,  by 
which  its  truth  is  evidently  demonstrated,  namely, 
to  suppose  certain  rudiments,  so  to  speak,  or 
beginnings  of  lines  and  figures,  less  than  any 
assignable."  So  that,  in  1671,  it  was  working  in 
Leibniz's  mind  that  in  the  doctrine  of  infinitely 
small  quantities  lay  the  true  foundation  of  that 
approach  to  the  differential  calculus  which  Cavalieri 
presented.1 

Dr  Gerhardt,  the  editor  of  the  correspondence 
already  referred  to,  found  among  the  papers  of 
Leibniz  preserved  in  the  Royal  Library  at  Hanover 
various  original  draughts,  containing  problems  in 
which  both  the  differential  and  integral  calculus  are 
employed,  and  has  published  them  in  a  separate 
tract.2  The  editor  dwells  so  much  on  the  matter 

1  [In  his  paper  "  On  the  Early  History  of  Infinitesimals  in  England," 
published   in   the   Philosophical  Magazine  for   November,    1852,  and 
mentioned  in  the  above  Preface,  De  Morgan  developed  his  thesis  that 
Fluxions  at  first  (up  to  1704)  had  an  infinitesimal  basis.     This  thesis 
is  supported  by  Newton's  own  early  papers  published  by  Rigaud  (see 
the  Appendix  to  this  Essay),  by  Newton's  Method  of  Fluxions^  by  the 
first  edition  of  the  Principia^  as  compared  with  the  second,  by  Newton's 
De   Quadratura    Curvarum,    by  works   of  John   Craig,   De    Moivre, 
Halley,  Cotes,  Cheyne,  and  Fatio  de  Duillier,  besides  the  books  by 
Harris  and  Hayes  mentioned  in  the  text  above.] 

2  Die   Entdeckung  der  Differentialrechnung  durch  Leibniz.       Von 
Dr   C.  J.    Gerhardt.     Quarto.     No   date  nor   place ;   preface   dated 
"Salzwedel,  im  Januar  1848:"  [Accordingly  we  must  conclude  that 
Gerhardt's  tract,  in  the  form  in  which  it  often  exists,  under  the  title 
Die  Entdeckung  der  Differentialrechnung  durch  Leibniz,  mit  Benutzung 
der    Leibnizischen    Manuscripte    auf  der  Koniglichen  Bibliothek  zu 
Hannover,  Halle,  1848,  has  a  different  title-page  from  the  one  seen  by 
De  Morgan,  which  was  probably  the  extract  it  was  from  the  Programm 
of  the  school  at  Salzwedel.     Two  years  earlier,  Gerhardt  had  published 
a  very  important  manuscript  of  Leibniz's  under  the  title  Historia  et 


CALCULUS  97 

and  consequences  of  the  manuscripts,  that  he  forgets 
to  satisfy  curiosity  as  to  their  form,  the  circumstances 
of  the  discovery,  and  so  on  :  they  ought  to  be  re- 
published  with  proper  facsimiles  of  the  handwriting. 
Not  that  we  at  all  doubt  them  ;  for,  independently 
of  the  full  credit  due  to  Dr  Gerhardt,  we  do  not 
believe  that  human  ingenuity  could  have  forged  so 
genuine  a  mess  of  spoiled  exercises.  We  cannot 
attempt  a  full  account  of  them  ;  but  this  is  of  little 
consequence,  since  they  will  of  necessity  be  fully 
described  in  more  appropriate  quarters,  so  soon  as 
they  are  better  known  to  exist. 

These  papers  are  seven  in  number,  dated  l  Novem- 
ber the  nth,  2 ist,  22nd,  1675,  June  the  26th,  July, 
November,  1676,  and  one  without  a  date.  They 
are  not  descriptions  of  the  principles,  but  study 
exercises 2  in  the  use,  of  both  differential  and 
integral  calculus.  Except  out  of  the  problems 
themselves,  we  learn  nothing  of  the  extent  to  which 

Origo  Calculi  Differentialis  a  G.  G.  Leibnitio  conscripta.  Zur  zweiten 
Sacularfeier  des  Leibnizischen  Geburtstages  aus  den  Handschriften  der 
Koniglichen  Bibliothek  zu  Hannover,  Hanover,  1846.  Further  infor- 
mation about  Gerhardt's  publications  on  Leibniz  is  given  in  the  Appendix 
to  this  Essay.] 

1  The  editor  tells  us  that  some  one  had  been  meddling  with  the  date 
of  the  first  paper,  and  had  turned  the  5  of  1675  into  a  3.     Leibniz, 
speaking  from  recollection  in  1714,  says  that  his  discovery  was  made, 
as  near  as  he  could  remember,  in  1676. 

2  Professor  Rigaud  has  published,  from  the  Macclesfield  collection, 
a  manuscript  draught  of  Newton,  of  November  I3th,   1665.     But  this 
is  formally  written  out,  proposition,  resolution,  and  demonstration.     An 
earlier  essay,  of  May  2Oth,  is  not  given,  which  is  to  be  regretted.     But 
from  the  description  we  see  that  Newton  used  the  peculiar  notation  of 
fluxions  in   May,  and   abandoned   it   in  November.     His  formal  pro- 
position uses  distinct  letters  for  fluxions  of  other  letters.     In  Leibniz, 
everything  in  language  is  progression  :  no  step  gained  is  ever  abandoned. 

7 


98  FLUXIONAL 

the  structural  operations  were  in  the  power  of  the 
writer.  We  find  strange  mistakes  of  operation, 
such  as  beginners  now  make  :  and  it  is  clear  that 
the  writer  is  trying  to  push  his  calculus  forward 
into  discovery  of  new  results  in  geometry  before 
he  has  either  sounded  its  extent  or  settled  its 
language.  In  the  first  of  the  papers  he  enters 
(among  other  things)  upon  the  examination  whether 

dx.dy  is  the  same  with  d(xy)  and  d(-)  with  — :  at 

\y'  dy 

first  he  inclines  to  the  affirmative,  but  in  the  next 
page  decides  in  the  negative.  This  will  not  surprise 
the  mathematician  of  our  day,  who  remembers  that 
these  are  the  private  memoranda  of  a  discoverer  in 
the  very  process  of  investigation  :  but  nevertheless 
he  will  look  to  find  some  particular  cause  of  con- 
fusion of  ideas  at  the  outset.  We  suspect  it  to  be 
as  follows.  Leibniz  frequently  supposes  dx=i,  or 
dy  =  i  :  that  is,  he  establishes  two  kinds  of  units, 
without  any  symbolic  distinction,  the  unit  of  finite, 
and  the  unit  of  infinitely  small,  quantity.  In  integra- 
tion, he  halts  between  the  use  of  I  y  and  oilydx, 

as  the  expression  of  an  integral.  There  are  also 
obvious  slips  of  the  pen,  and  operations  set  down 
for  thought,  which  lead  to  nothing. 

The  first  problems  treated  are  in  the  direct  and 
inverse  method  of  tangents,  in  which  the  method  of 
Sluse  is  referred  to  by  name.  The  two  following 


CALCULUS  99 

extracts,  in  which  the  Latin  is  literally  translated, 
of  the  date  of  November  the  nth,  1675,  will  be  as 
much  as  we  can  afford  room  for.  They  give  two 
of  the  earliest  problems  solved,  the  first  and  third. 

The  problem  is  to  find  a  curve  in  which  the 
subnormal  (w)  is  reciprocally  proportional  to  the 
ordinate.  Putting  z  instead  of  dx,  Leibniz  proceeds 
thus  : — "  It  appears  from  what  I  have  shown  else- 


f  ••'-••••  V  V 

where,   that  /«/£=<-,  or  w %  =  -?—-"      The  d  in  the 

denominator  is  the  symbol  of  differentiation  of  the 
whole  :  it  frequently  happens  in  the  first  papers. 
1 '  But  from  the  quadrature  of  the  triangle  this  is 
y."  We  should  write  ydy,  but  Leibniz  tacitly  makes 
dy=it  and  he  afterwards  says  he  has  here  thought 
of  making  an  abscissa  of  the  ordinate.  "  Now  from 

the  hypothesis  w  =  -  .   .   .   whence  —  =i/,  and  #=•?-. 
y  y  b 

But  [z=x.     Therefore;^  $L     But  &m£*  by  the 
}  J  b  J  b      $da 

i/3 
quadrature  of  the  parabola  ;  therefore  x— -^—. "     This 

a  is  not  of  easy  explanation.  It  is  afterwards  given 
to  make  the  subnormal  reciprocally  proportional  to 

a2  [        v2 

the  abscissa.      ''Here  «;  =  — ;   but  \w  =  —  y  whence 

X  J  2 

y=/y/(2jWj  or  fj(2\(—\t      Now  \w  cannot  be  found 

except  by  the  help  of  the  logarithmic  curve.  There- 
fore the  figure  required  is  that  in  which  the  ordinates 


ioo  FLU XI  ON AL 

are  in  the  subduplicate  ratio  of  the  logarithms  of 
the  abscissae." 

If  the  Committee  of  the  Royal  Society  had  had 
these  papers  before  them,  they  would  have  justly 
contended  that  the  calculus  of  Leibniz,  of  which 
the  principles  and  algorithm  were  settled,  received 
a  great  accession  of  working  power  when  Newton 
communicated  the  binomial  theorem  in  the  "  epistola 
prior"  to  Oldenburg;  which  "epistola  prior,"  by 
the  rule  of  contraries  already  instanced,  has  been 
much  less  insisted  on  than  the  "epistola  posterior" 
with  its  anagrams. 

On  August  the  27th,  1676,  Leibniz  acknowledged 
the  receipt  of  this  communication  ;  and  his  paper  of 
November  1676  shows  that  Newton's  algebra  had 
borne  its  fruit.  Previously  to  this  date,  we  cannot 
find  any  fractional  power  differentiated  except  the 
square  root.  In  pure  algebraical  discovery,  Leibniz 
does  not  rank  with  Newton  :  and  he  always  acknow- 
ledged that  in  the  method  of  series  (the  phrase  by 
which  the  algebraical  improvements  of  the  day 
were  designated)  Newton  was  before  him  and 
beyond  him.  We  have  every  right  to  presume, 
from  his  conduct,  and  from  the  manner  in  which 
all  subsequent  disclosures  establish  his  veracity, 
that  had  he  lived  to  publish  his  own  Commercium 
Epistolicum,  he  would  have  pointed  out  the  difference 
between  the  invention  of  the  differential  calculus 
and  the  improvement  of  the  algebra  which  gives  it 


CALCULUS',:  v\      vi'   10 1 


language  and  guides  its  nteehamsiJV  afl,d 
illustrated  from  his  own  papers  the  power  which 
Newton's  improvements  in  algebra  enabled  him  to 
add  to  his  existing  differential  calculus.  We  believe 
(with  John  Bernoulli)  that  Newton  might  have  made 
a  similar  acknowledgment  to  Leibniz  as  to  the 
idea  of  a  fixed  and  uniform  method  of  denoting 
operations  in  the  fluxions  of  which  he  had  already 
possession. 

We  have  not  alluded  to  the  faults  on  the  other 
side  of  the  controversy,  partly  because  they  were 
much  less  gross  in  character,  partly  because  they 
have  been  amply  insisted  on  in  this  country.  Nor 
have  we,  indeed,  in  this  paper,  given  anything  like 
a  history  of  the  unfair  proceedings  in  this  country, 
but  have,  for  the  most  part,  confined  ourselves  to 
points  which  are  particularly  effected  by  recent 
information.  Whether  there  be  anything  still  to 
be  drawn  out  must  be  matter  of  conjecture,  and  will 
be  matter  of  suspicion,  until  we  can  be  well  assured 
that  all  the  private  depositories  of  information  have 

been  exhausted. 

A.  DE  MORGAN. 

UNIVERSITY  COLLEGE,  LONDON, 
October  2,  1851. 


APPENDIX1  ON  THE  MANUSCRIPTS  AND 
PUBLICATIONS  OF  NEWTON  AND 
LEIBNIZ 

IN  this  Appendix  is  given,  in  chronological  order,  a  list  of 
the  manuscripts  and  other  works  of  Newton  and  Leibniz 
relating  to  the  discovery  and  communication  of  the  in- 
finitesimal calculus  and  publications  dealing  with  the  con- 
troversy that  subsequently  took  place  between  them  and 
their  respective  supporters.  References  have  been  given  on 
each  point,  and  it  is  hoped  that  both  the  list  and  the  refer- 
ences are  complete  in  the  sense  that  nothing  important  has 
been  omitted.  It  is  rather  remarkable  that  nothing  has 
hitherto  been  done  in  this  direction,  for  it  would  seem  to  be 
very  important  that  regard  be  paid  to  Newton's  early  manu- 
scripts. Many  important  manuscripts  of  Leibniz's  which 
relate  to  his  discovery  have  been  published  by  Gerhardt, 
and  commented  on  by  Gerhardt  and  others ;  but  only  a  few 
of  Newton's  manuscripts  have  as  yet  been  published,  and 
these  publications — by  Raphson  in  1715  and  Rigaud  in 
1838 — have  apparently  been  completely  ignored  by  all  the 
modern  historians  of  mathematics.  After  a  list  of  works 
consulted,  together  with  some  brief  comments  on  some  of 
them  and  the  abbreviations  by  which  their  titles  are  cited  in 
this  Appendix,  are  given  :  (i)  References  on  the  history  of 
infinitesimal  ideas  before  Newton  and  Leibniz ;  (2)  Refer- 
ences to  Newton's  fluxional  manuscripts  and  publications ; 
(3)  References  to  Leibniz's  manuscripts  and  publications  on 

1  The  whole  of  this  Appendix  is  by  the  Editor  of  the  present  collec- 
tion of  Essays  by  De  Morgan,  and  is  supplementary  to  the  second  Essay. 

102 


NEWTON  AND  LEIBNIZ  103 

the  infinitesimal  calculus;  and  (4)  Brief  references  to  the 
literature  of  the  controversy  about  the  invention  of  the 
calculus.  It  is  hoped  that  this  Appendix  will  be  gradually 
made  complete,  either  in  future  editions  of  the  present  book 
or  as  a  separate  publication. 

WORKS  CONSULTED,  WITH  ABBREVIATIONS 

MORITZ  CANTOR  :  Vorlesungen  iiber  Geschichte  der  Mathe- 
matik;  vol.  i  (to  A.D.  1200),  3rd  ed.,  Leipsic,  1907; 
vol.  ii  (1200-1668),  2nd  ed.,  Leipsic,  1900;  vol.  iii 
(1668-1758),  2nd  ed.,  Leipsic,  1901  (contains  an 
account  of  Leibniz's,  but  not  of  Newton's,  manuscripts). 
Abbreviation :  Cantor. 

KARL  FINK  :  Geschichte  der  Elementar-Mathematik :  trans- 
lated by  W.  W.  Beman  and  D.  E.  Smith  under  the 
title  A  Brief  History  of  Mathematics  (Chicago,  3rd 
ed.,  1910;  pp.  168-172  contain  a  brief  summary  of 
the  origin  and  discovery  of  the  infinitesimal  calculus). 

W.  W.  ROUSE  BALL  :  A  Short  Account  of  the  History  of 
Mathematics^  London,  4th  ed.,  1908.  In  this  work, 
a  whole  chapter  (pp.  319-352)  is  devoted  to  "The  Life 
and  Works  of  Newton,"  in  which  Newton's  early  manu- 
scripts are  referred  to,  but  without  references,  and  in 
this  chapter  the  communications  with  Leibniz  are  dis- 
cussed; but  the  controversy  is  dealt  with  when  an 
account  of  Leibniz's  work  is  given  (pp.  353-365),  where 
Leibniz's  manuscripts  are  hardly  referred  to,  and  he 
himself  is  treated  with  suspicion. 

JOSEPH  RAPHSON  :  The  History  of  Fluxions,  shewing  in  a 
compendious  manner  the  first  rise  of  and  various  improve- 
ments made  in  that  incomparable  Method,  London,  1715. 
A  Latin  translation  was  published  at  London  in  the 
same  year  (see  G.  J.  Gray's  work  mentioned  below, 
p.  54).  Abbreviation  :  Raphson. 

STEPHEN   PETER   RIGAUD  :   Historical  Essay  on  the  First 


104  DISCOVERIES    OF 

Publication  of  Sir  Isaac  Newton's  Principia,  Oxford, 
1838.  In  this  book,  the  pages  of  the  text  of  the  first 
part  and  those  of  the  Appendix  are  numbered  separately. 
In  the  Appendix  are  given  some  of  Newton's  early 
manuscripts  on  fluxions  from  the  collection  of  Lord 
Macclesfield.  Abbreviation :  Rigaud. 

STEPHEN  PETER  RIGAUD  :  (though  Rigaud's  name  does  not 
appear  on  the  title-page,  it  was  he  who  made  this 
collection)  Correspondence  of  Scientific  Men  of  the  Seven- 
teenth Century ',  including  Letters  of  Barrow,  Flamsteed, 
Wallis,  and  Newton,  printed  from  the  Originals  in  the 
Collection  of  the  Right  Honourable  the  Earl  of  Maccles- 
field. Two  volumes  (posthumous,  edited  by  Rigaud's 
son,  Stephen  Jordan  Rigaud),  Oxford,  1841.  Table 
of  contents  and  index  added  by  De  Morgan  (see  Mrs 
De  Morgan's  Memoir,  p.  414)  in  1862.  Fifty-nine 
letters  from  and  to  Newton,  beginning  in  1669,  were 
published  on  pp.  281-437  of  vol.  ii.  Abbreviation  : 
Mace.  Corr. 

J.  EDLESTON  :  Correspondence  of  Sir  Isaac  Newton  and 
Professor  Cotes,  including  Letters  of  Other  Eminent 
Men,  now  first  published  from  the  originals  in  the 
Library  of  Trinity  College,  Cambridge',  together  with 
an  Appendix  containing  other  unpublished  Letters  and 
Papers  by  Newton  ;  with  Notes,  Synoptical  View  of  the 
Philosopher's  Life,  and  a  Variety  of  Details  illustrative 
of  his  History,  London  and  Cambridge,  1850.  Ab- 
breviation :  Edleston. 

Sir  DAVID  BREWSTER  :  Memoirs  of  the  Life,  Writings,  and 
Discoveries  of  Sir  Isaac  Newton,  2  vols.,  Edinburgh, 
1855.  A  second  edition — apparently  unaltered,  even 
as  to  the  mistakes — was  published  at  Edinburgh,  1860. 
Abbreviation  (to  the  1855  edition) :  Brewster. 

A  Catalogue  of  the  Portsmouth  Collection  of  Books  and 
Papers,  written  by  or  belonging  to  Sir  Isaac  Newton, 
the  Scientific  Portion  of  which  has  been  presented  by  the 


NEWTON  AND  LEIBNIZ  105 

Earl  of  Portsmouth  to  the  University  of  Cambridge. 
This  catalogue  was  drawn  up  by  the  Syndicate 
appointed  the  6th  of  November,  1872,  and  the  Preface 
is  signed  by  H.  R.  Luard,  G.  G.  Stokes,  J.  C.  Adams, 
and  G.  D.  Liveing,  and  published  at  Cambridge  in 
1888.  Abbreviation:  Portsmouth  Catalogue. 

G.  J.  GRAY  :  A  Bibliography  of  the  Works  of  Sir  Isaac 
Newton  together  with  a  List  of  Books  illustrating  his 
Works.  Second  edition,  Cambridge,  1907.  The  first 
(and  less  full)  edition  was  privately  printed  in  1888. 
Abbreviation :  Gray. 

FERDINAND  ROSENBERGER  :  Isaac  Newton  und  seine  physika- 
lischen  Principien.  Ein  Hauptstiick  aus  der  Entwicke- 
lungsgeschichte  der  modernen  Physik.  Leipsic,  1895. 
Abbreviation  :  Rosenberger. 

C.  I.  GERHARDT  (herausgegeben  von) :  Historia  et  Origo 
Calculi  Differential  a  G.  G.  Leibnitio  conscripta.  Zur 
zweiten  Sdcularfeier  des  Leibnizischen  Geburtstages  aus 
den  Handschriften  der  Koniglichen  Bibliothek  zu  Hann- 
over >  Hanover,  1846.  Abbreviation  :  G.  1846. 

C.  J.  GERHARDT  :  Die  Entdeckung  der  Differentialrechnung 
durch  Leibniz,  mit  Benutzung  der  Leibnizischen  Manu- 
scripte  auf  der  Koniglichen  Bibliothek  zu  Hannover, 
Halle,  1848.  Abbreviation:  G.  1848. 

C.  I.  GERHARDT  :  Die  Geschichte  der  hoheren  Analysis. 
Erste  Abtheilung  [the  only  one  which  appeared] ;  Die 
Entdeckung  der  hoheren  Analysis,  Halle,  1855.  Ab- 
breviation :  G.  1855. 

HERMANN  WEISSENBORN  :  Die  Principien  der  hoheren 
Analysis  in  ihrer  Entwicklung  von  Leibniz  bis  auf 
Lagrange,  als  ein  historisch-kritischer  Beitrag  zur  Ge- 
schichte der  Mathematik  dargestellt,  Halle,  1856.  Ab- 
breviation :  W.  1856.  A  further  contribution  of 
Weissenborn's  is  dealt  with  below. 

Die  philosophischen  Schriften  von  G.  W.  Leibniz,  herausge- 
geben von  C.  J.  Gerhardt,  7  vols.,  Berlin,  1875-90. 


106  DISCOVERIES    OF 

Leibnizens  mathematische  Schriften,  herausgegeben  von  C.  J. 
Gerhardt,  7  vols.,  Berlin  and  Halle,  1849-1863.  The 
contents  of  these  volumes  are  described  in  note  3  on 
pp.  71-72. 

Der  Brief wechsel  von  Gottfried  Wilhelm  Leibniz  mit  Mathe- 
matikern,  Herausgegeben  von  C.  I.  Gerhardt,  vol.  i, 
Berlin,  1899.  Leibniz's  manuscripts  of  October,  1675, 
are  dealt  with  on  pp.  xii-xiv,  and  those  of  November 
1675  and  July  1676  on  pp.  xiv-xv.  Leibniz's  relations 
with  Tschirnhaus  are  dealt  with  on  pp.  xvii-xviii.  Cf. 
note  i  on  p.  79.  The  volume  contains  the  correspond- 
ence between  Leibniz  and  Oldenburg,  Newton,  Collins, 
and  Conti,  from  1670  to  1716,  and  also  many  supple- 
mentary documents.  Among  these  are  reproduced 
(pp.  147-167)  some  of  Leibniz's  manuscripts  of  1675 
and  (pp.  201-203)  one  of  July  1676,  which  are  referred 
to  in  the  list  given  below.  In  the  valuable  introduction 
(pp.  3-38)  to  this  correspondence,  Leibniz's  mathe- 
matical work  from  1669  onwards  is  dealt  with  on  pp.  5- 
38.  Mention  is  made  of  Die  philosophischen  Schriften 
von  G.  W.  Leibniz,  but  not  of  Leibnizens  mathematische 
Schriften,  nor  of  G.  1846,  G.  1848,  and  G.  1855. 
Abbreviation  :  Bw.  1899. 

G.  E.  GUHRAUER  :  Gottfried  Wilhelm  Freiherr  von  Leibnitz  : 
Eine  Biographic,  2  volumes,  Breslau,  1846. 

L£ON  BRUNSCHVICG  :  Les  Stapes  de  la  Philosophic  mathe- 
matique,  Paris,  1912.  The  third  book  (pp.  153-249) 
contains:  (i)  A  sketch  of  the  growth  of  infinitesimal 
ideas  from  ancient  times ;  (2)  Accounts  of  the  dis- 
coveries of  Leibniz  and  Newton  in  the  domain  of  the 
infinitesimal  analysis,  in  which,  however,  almost  no 
account  is  taken  of  the  manuscripts  of  Leibniz  and 
none  of  those  of  Newton  ;  (3)  An  account  of  Leibniz's 
mathematical  philosophy ;  (4)  A  discussion  of  mathe- 
matical idealism  and  metaphysical  realism. 


NEWTON  AND   LEIBNIZ  107 


I 

INFINITESIMAL  IDEAS  BEFORE  THE  TIME  OF  NEWTON 
AND  LEIBNIZ 

Euclid,  Archimedes,  Pappus,  Arabians,  Middle  Ages  and 
Renascence,  Valerius,  Kepler,  Cavalieri,  Torricelli,  Fermat, 
Roberval,  Pascal,  Wallis,  Mercator,  St  Vincent,  Descartes, 
Huygens,  Sluse,  Hudde,  Barrow  :  Cantor^  vols.  i  to  iii  ; 
Brews  ter,  vol.  ii,  pp.  3-9  ;  G.  1855,  PP-  3~5° ;  Rosenberger, 
pp.  424-430.  Cf.  also  W.  1856,  pp.  5-21  (Roberval  and 
Barrow  as  precursors  in  the  method  of  fluxions),  and  pp. 
70-84  (Gregorius  a  St.  Vincent,  Barrow,  etc.,  as  precursors 
of  the  differential  calculus).1 


II 

NEWTON'S  MANUSCRIPTS  AND  PUBLICATIONS  ON  THE 
FLUXIONAL  CALCULUS 

Newton's  early  study  of  mathematics  at  Cambridge  in  the 
years  1661-4  is  dealt,  with  by  Brewster  (vol.  i,  pp.  21-23). 
Having  read  Descartes,  Schooten,  and  Wallis,  Newton  (MS. 
note  of  1699,  given  in  ibid.t  pp.  23-24)  found  the  method 
of  infinite  series  in  1664-5,  and,  in  the  summer  of  1665, 
computed  the  area  of  the  hyperbola  at  Boothby  in  Lincoln- 
shire to  fifty-two  places  by  this  method.2  Cf.  Brewster,  vol. 

1  The   subsequent  history   of  the  principles  of  the  calculuses   with 
Maclaurin,  the  Bernoullis,  Neuwentiit,  Taylor,  Euler,  and  Lagrange 
are  also  dealt  with  in  the  book  mentioned. 

2  Among  the  "Portsmouth  Papers  "  (Section  I.    "  Early  Papers  by 
Newton")  is  this  calculation  of  the  area  of  the  hyperbola  {Portsmouth 
Catalogue,  p.  i).     All  the  papers  of  Newton  on  fluxions  in  this  collec- 
tion, many  of  which  it  would  be  important  to  publish,  are  catalogued 
on  pp.  1-8  of  this  Catalogue.     The  "  Early  Papers"  also  include  a  little 
note  on  tangents,  a  tract  written  in  1666  on  the  solution  of  problems  by 
motion,  on  the  gravity  of  conies,  and  problems  about  curves.     There 
are   also   manuscripts   on  "  Elementary  Mathematics,"  which  include 
"Observations  on    the   Algebra  of  Kinckhuysen"  (ibid.,  p.  2);   and 
several  manuscripts  on  fluxions  and  their  geometrical  and  mechanical 


1 08  DISCOVERIES    OF 

ii,  p.  10.  See  also  G.  1855,  pp.  90-92.  In  the  following 
list  of  manuscripts  use  has  been  made  of  the  "Synoptical 
Life  "  in  JEdleston,  pp.  xxi-lviii. 

1665,  May  2oth.  Paper  on  fluxions  in  which  the  nota- 
tion of  dots  is  used.  It  shows  how  to  take  the  fluxion  of 
an  equation  containing  any  number  of  variables.  It  is  re- 
ferred to  in  a  paper  which  seems  to  be  part  of  a  draft  of 
Newton's  observations  on  Leibniz's  letter  of  April  9th,  1716. 
Rigaud,  Appendix,  p.  23;  Raphson,  p.  116;  Brewster, 
vol.  i,  p.  25,  vol.  ii,  p.  12. 

1665,  Nov.   1 3th.    Paper  on   fluxions  and  their  applica- 
tions  to   tangents  and  curvature  of  curves.     Rigaud,  Ap- 
pendix,  No.  II,  pp.  20-23  (printed   at  length);   Raphson 
and  Brewster,  as  before.     Horsley,  in  vol.  iv  (p.  611)  of 
his  edition  of  Newton's  collected  works,  gives  this  paper, 
from    Raphson.     It  may  be  mentioned  that,  according  to 
Lord  Teignmouth's  Life  of  Sir  William  Jones  (p.  8),  Newton 
saw  the  first  sheets  of  Raphson's  History  and  was  much  dis- 
satisfied with  them. 

1666,  May  1 6th.    Another  paper   on   fluxions   (Rigaud) 
Appendix,  p.  23;  Brewster^  vol.  i,  p.  25,  vol.  ii,  p.  12). 

1666,  October.  Small  tract  on  fluxions  and  fluents,  with 
their  applications  to  a  variety  of  problems  on  tangents, 
curvature,  areas,  lengths,  and  centres  of  gravity  of  curves. 
In  this  tract,  Newton's  previous  method  of  taking  fluxions 
is  extended  to  surds.  The  area  of  a  curve  whose  ordinate 
is  y  is  denoted  by  a  small  square  prefixed  to  the  letter  y. 
Cf.  Rigaud^  Appendix,  pp.  23-24;  Brewster,  vol.  i,  p.  25, 
vol.  ii,  pp.  12-14.  These  early  papers  are,  as  De  Morgan 
remarked  (see  the  second  Essay),  infinitesimal  in  character. 
They  are  all  in  the  Macclesfield  Collection  (Brewster^  vol.  i, 
p.  25,  note  3). 

1666,   November,    Tract   similar   to   the   preceding,  but 

applications,  on  the  quadrature  of  curves,  and  on  the  fluxional  contro- 
versy (ibid.,  pp.  2-8).  One  of  the  papers  on  fluxions  was  marked  by 
Horsley  as  "  very  proper  to  be  published  "  (ibid.,  p.  2). 


NEWTON  AND   LEIBNIZ  109 

apparently  more  comprehensive  (Raphson,  p.  116;  Wilson's 
Appendix  to  Robins's  Tracts,  vol.  ii,  pp.  351-356).  Nota- 
tion by  dots  for  first  and  second  fluxions.  Basis  of  his 
larger  tract  of  1671. 

1669,  July  3 1  st.  De  Analyst  sent  through  Barrow  to 
Collins.  Cf.  Brewster,  vol.  ii,  pp.  14-15. 

This  seems  a  good  place  to  give  references  to  places 
where  Newton's  tract,  Analysis  per  aquationes  numero 
terminorum  infinitas,  was  published  or  discussed.  It  was 
first  published  at  London  in  1711,  and  reprinted  in  1712 
(Gray,  p.  59),  in  1723  (ibid.,  p.  10),  in  1744  (ibid.,  p.  2), 
and  in  vol.  i  (1779)  of  Horsley's  edition  of  Newton's  Opera. 
An  English  translation,  with  a  commentary,  was  made  by 
John  Stewart  in  1745  (ibid.,  p.  60).  See  also  Cantor, 
vol.  iii,  pp.  67-75,  105-108,  156-160;  Rosenberger,  pp. 
431-434;  R.  Reiff,  Gcschichte  der  unendlichen  Reihen, 
Tubingen,  1889,  pp.  20-38;  and  Brill  in  A.  Brill  and  M. 
Noether's  report :  "  Die  Entwicklung  der  Theorie  der 
algebraischen  Functionen  in  alterer  und  neuerer  Zeit," 
Jahresber.  der  Deutschen  Mathcm.-Vereinigung,  vol.  iii,  1894, 
pp.  116-123. 

1669,  December.  Newton  writes  notes  upon  Kinckhuysen's 
Algebra  sent  by  Collins  through  Barrow  (Brewster,  vol.  i, 
pp.  68-69,  vol.  ii,  pp.  15-16;  G.  1855,  P-  83). 

Newton's  letters  to  Collins  reporting  progress  on,  and 
comments  on,  Kinckhuysen's  Algebra  are  given  in  Mace. 
Corr.,  and  are  mentioned  by  Edleston  under  the  dates  of 
Jan.  1 9th,  Feb.  6th,  Feb.  i8th,  July  nth,  July  i6th,  and 
Sept.  27th,  1670.  See  also  Brewster,  vol.  i,  p.  69.  A 
reference  to  his  "  discourse  on  infinite  series "  occurs  in 
a  letter  to  Collins,  mentioned  by  Edleston,  of  July  2oth, 
1676. 

Towards  the  end  of  1671,  Newton  was  occupied  in 
enlarging  his  method  of  infinite  series  and  preparing  twenty 
optical  lectures  for  the  press.  The  method  was  never 
finished.  It  was  published  by  Horsley  (vol.  i,  pp.  391-518) 


no  DISCOVERIES    OF 

under  the  title  of  "  Geometria  Analytica."  It  first  appeared 
in  1736  in  Colson's  translation;  see  Pemberton's  preface  to 
his  View  of  Newton's  Philosophy,  London,  1728.  See  also 
Cantor,  vol.  iii,  pp.  168-179,  108-109;  Brewster,  vol.  ii, 
pp.  15-16;  Rosenberger,  pp.  434-438;  Gray,  pp.  46-48, 

I,    2. 

Newton's  Tractatusde  Quadratura  Curvarum(o,i.  Brewster 
vol.  ii,  pp.  17-18)  was  printed  at  the  end  of  the  first  edition 
of  the  Opticks  (London,  1704,  cf.  Gray,  pp.  35-36,  37-38). 
Extracts  from  the  work  had  previously  been  printed  in  John 
Wallis's  Opera  Mathematica,  of  which  four  volumes  were 
published  at  Oxford  from  1693  to  1699.  For  other  editions, 
see  Gray,  pp.  59,  i,  2.  An  English  translation  of  it  was 
published  by  John  Stewart  in  1745  (ibid.,  p.  60),  and  a 
German  annotated  translation  by  G.  Kowalewski  is  in  No. 
164  of  Ostwald's  Klassiker.  On  Newton's  fluxional  works, 
see  W.  1856,  pp.  21-58. 

In  a  letter  of  May  25th,  1672,  to  Collins,  Newton  said 
that  he  did  not  intend  to  publish  his  lectures,  but  might 
possibly  complete  his  method  of  infinite  series,  "  The  better 
half  of  which  was  written  last  Christmas"  (Mace.  Corr., 
vol.  ii,  p.  332). 

1672,  Dec.  loth.  Letter  to  Collins'containing  an  account, 
requested  by  Collins  in  a  letter  received  two  days  before,  of 
his  method  of  tangents  (see  Edleston,  note  35  on  p.  xlvii). 

1673,  June  23rd.  Letter  to  Oldenburg  on  Slusius's  method 
of  tangents  (see  Edleston,  p.  251). 

1675.  In  a  letter  of  Collins  to  James  Gregory,  dated  Oct. 
i9th,  1675.  "Mr  Newton  ...  I  have  not  writ  to  or  seen 
these  eleven  or  twelve  months,  not  troubling  him  as  being 
intent  upon  chemical  studies  and  practices,  and  both  he  and 
Dr  Barrow  beginning  to  think  mathematical  speculations  to 
grow  at  least  dry,  if  not  somewhat  barren"  (Mace.  Corr., 
vol.  ii,  p.  280). 

1675,  Jan-  22nd.  Letter  to  Michael  Dary  on  length  of  an 
elliptic  arc. 


NEWTON  AND  LEIBNIZ  in 

1676,  June  1 3th.  Letter  to  Oldenburg,  containing  a 
general  answer  to  Lucas  and  "some  communications  of 
an  algebraic  nature  for  M.  Leibnitz,  who  by  an  express 
letter  to  Mr  Oldenburg  had  desired  them."  The  part  for 
Leibniz  was  sent  to  him  at  Paris,  July  26th,  and  was  after- 
wards printed  in  Wallis's  Opera,  vol.  iii,  pp.  622-629,  and 
from  that  work  in  the  Comm.  Epist.,  where  the  typo- 
graphical error  of  "  26  Junii "  for  "  Julii,"  which  is  corrected 
in  Wallis's  Errata,  is  also  copied  in  the  heading  of  the 
letter.  Cf.  second  Essay,  above. 

1672,  Sept.  5th.  Letter  to  Collins  (infinite  series  of  no 
great  use  in  the  numerical  solution  of  equations.  The 
University  Press  cannot  print  Kinckhuysen's  Algebra ;  the 
book  is  in  the  hands  of  a  Cambridge  bookseller  with  a  view 
to  its  being  printed :  shall  add  nothing  to  it.  Will  alter 
an  expression  or  two  in  his  paper  about  infinite  series,  if 
Collins  thinks  it  should  be  printed). 

1676,  Oct.  24th.  Latin  letter  to  Oldenburg  for  Leibniz, 
who  desired  explanation  with  reference  to  some  points  in 
the  letter  of  June  i3th.  See  note  55  in  Edleston,  pp.  li-lii. 

1676,  Oct.  26th.  Letter  to  Oldenburg  with  corrections 
for  his  letter  of  Oct.  24th.  See  note  56  in  Edleston,  p.  Hi. 

1676,  Nov.  8th.  Letter  to  Collins  thanking  him  for 
copies  of  the  letters  of  Leibniz  and  Tschirnhaus,  with 
remarks  showing  that  Leibniz's  method  is  not  more  general 
or  easy  than  his  own  (Maa.  Corr.,  vol.  ii,  p.  403). 

1676,  Oct.  i4th.  Letter  to  Oldenburg  (further  alterations 
of  his  letter  of  Oct.  24th).     Cf.  note  58  of  Edleston,  p.  Hi. 

1677,  March  5th.  Letter  of  Collins  to  Newton,  printed  in 
Wallis's   Opera,  vol.  iii,  p.    646    (extracts   from   it   in   the 
Comm.  Epist.}. 

1687.  Method  for  finding  volume  of  a  segment  of  a 
parabolic  conoid  (Edleston,  end  of  note  90  on  p.  Iviii). 

1692,  August  27th  and  Sept.  i7th.  Letters  to  Wallis, 
with  illustrations  of  the  calculus  of  fluxions  and  fluents 
tsent  at  Wallis's  request  (Wallis,  Opera,  vol.  ii,  p.  391). 


ii2  DISCOVERIES    OF 

1693,  March  i/|.th.  Letter  to  Fatio  (proposing  to  make 
him  such  an  allowance  as  might  make  his  subsistence  at 
Cambridge  easy  to  him ;  Edleston^  note  108  on  p.  Ix). 

1693,  Oct.  1 6th.  Letter  to  Leibniz  (Edleston,  pp.  276- 
279). 

1697,  Jan.  3oth.  Solution  of  John  Bernoulli's  two 
problems  (Edleston,  note  128  on  p.  Ixviii) :  read  to  the 
Royal  Society  Feb.  24th,  and  printed  without  Newton's 
name  in  the  Philosophical  Transactions  for  January. 

1704.  Equivocal  expressions  in  the  review  of  Newton's 
tract,  De  Quadratura  Curvarum  in  the  Leipsic  Acts 
(Edleston,  note  1 48  on  pp.  Ixxi-lxxiii).  This  was  the  origin 
of  the  dispute  as  to  priority. 

Ill 

LEIBNIZ'S  MANUSCRIPTS  AND  PUBLICATIONS  ON 
THE  INFINITESIMAL  CALCULUS 

Development  of  Leibniz's  mathematical  education. 
G.  1848,  pp.  7-20  (also  on  Descartes,  Fermat,  and  others), 
29-32 ;  G.  1855. 

Leibniz's  first  discoveries  in  mathematics  (Pascal's 
influence,  G.  1846,  pp.  1-20  (Hist,  et  origo;  see  notes 
21-31)  ;  G.  1855,  p.  33 ;  Leibniz  and  St  Vincent,  G-  1855, 
pp.  37-38;  Leibniz  and  Barrow,  G.  1855,  P-  4^ ;  G.  1848^ 
p.  15).  Cf.  also  Cantor,  vol.  iii,  pp.  76-84,  161-164; 
Rosenberger,  pp.  438-441. 

Leibniz's  manuscripts.1 

1673,  August.  Method  of  tangents  (inverse  problem  also 
dealt  with).     G.  1855,  pp.  55-57  ;  G.  1848,  pp.  20-22. 

1674,  October.     Inverse  problem  is  that  of  quadratures. 
G.  1855,  P-  57 ;  G.  1848,  p.  22. 

1674,  October.  Summation  of  series.  G.  1855,  pp.  57- 
58;  G.  1848,  pp.  22-23. 

1  If  the  manuscript  is  printed  at  length,  it  is  stated  so  explicitly. 
On  the  genuineness  of  the  dates,  see  G.  1848,  p.  6. 


NEWTON  AND  LEIBNIZ  113 

1675,  January.  Descartes'  method  not  sufficient  for 
inverse  problem.  G.  1855,  p.  58  ;  G.  1848,  pp.  23-24. 

1675,  Oct-  25tn-  Method  of  quadrature.  G.  1855,  pp. 
58,  117-119  (printed  in  full);  Bw.  1899,  pp.  147-149 
(printed  in  full). 

1675,  Oct.  26th.  The  same  subject.  G.  1855,  pp.  58, 
119-121  (printed  in  full);  Bw.  1899,  pp.  149-151  (printed 
in  full). 

1675,  Oct.  29th.    The  same  subject  (uses  J  ).     G.  1855, 

PP-  58~59>  121-127,  161-162;  Bw.  1899,  pp.  151-156. 

1675,  Nov.  ist.  The  same  subject.  G.  1833,  pp.  60, 
127-131  ;  Bw.  1899,  pp.  157-160. 

I675,1  Nov.  nth.  Example  of  the  inverse  method  (d 
used).  G.  1855,  pp.  160-161,  132-139;  G*  1848,  pp. 
23-24,  32-40;  Bw.  1899,  pp.  161-167. 

1675,  Nov.  2 1 st.  On  d  (xy).  G.  1853,  pp.  62-63; 
G.  1848,  pp.  4i-45>  24-25. 

1675,  Nov.  22nd.     Problem  of  tangents.     G.  1848,  pp.  25, 
46-48. 

1676,  June  1 6th.     Direct  problem  of  tangents  can  also 
be    treated.      G.   1855,    pp.    63-64;    G.   1848,   pp.   49- 
5°>  25. 

1676,  July.  G.  1848,  pp.  25-26,  51-54;  Bw.  1899,  pp. 
201-203. 

1676.  Leibniz  in  England,  Holland;  and  Germany.  G. 
1848,  pp.  54-56  (Bw.  1899,  pp.  228-230),  26-27. 

1676,  Nov.     Differential  calculus  of  tangents.     G.  1855, 
pp.  65,  140-142;  G.  1848,  pp.   27,  56-59;  Bw.  1899,  pp. 
229-231. 

1677.  Correspondence  with  Newton. 

1677,  July  n.  Tangents  (for  publication).  G.  1835^ 
pp.  66,  143-148;  G.  1848,  pp.  27-28,  59-65. 

1684.  Leibniz's  publication;  his  relations  with  Tschirn- 
haus.  G.  1855,  pp.  66-72  ;  G.  1848,  p.  28. 

1  Here  somebody  has  tried  to  turn  the  5  into  a  3. 

8 


ii4  DISCOVERIES    OF 

MS.  "Elementa  calculi  novi  .  .  .  ,"  G.  1855 ',  pp.  72, 
i49-J55;  G.  1846,  pp.  32-38. 

Another  MS.,  G.  1846,  pp.  39-50. 

On  Leibniz's  manuscripts,  see  also  Cantor,  vol.  iii,  pp. 
164-168;  Rosenberger,  p.  447,  note;  and  W.  1856,  pp. 
84-115, 

Gerhardt1  published  a  note  on  the  history  of  the  con- 
troversy about  the  first  discovery  of  the  differential  calculus, 
together  with  some  critical  remarks  on  Weissenborn's  book. 

In  Weissenborn's  book  reference  was  often  made  to  an 
essay  of  his  in  explanation  of  some  points  in  Leibniz's 
manuscripts  in  Vol.  XXV  of  Grunerts  Archiv.  As  this 
essay  did  not  appear,  Weissenborn  published  the  most 
important  part  of  it  under  the  title  "  Bemerkungen  zu 
einigen  in  Dr  C.  J.  Gerhardt's  '  Entdeckung  der  hoheren 
Analysis '  verorfentlichten  Manuscripten  Leibnizens "  in 
SchlomilcKs  Zeitschrift  for  1 856.2  This  should  be  read  in 
connection  with  Gerhardt's  publications. 

On  the  letters  and  publications  of  Newton  and  Leibniz, 
see  Cantor,  vol.  iii,  pp.  179-215,  and  Rosenberger,  pp.  441- 
455.  Leibniz's  publications  are  reprinted  in  Vol.  V  of  his 
Mathematische  Schriften  edited  by  Gerhardt  (see  note  3  on 
pp.  71-72);  and  annotated  German  translations,  by  G. 
Kowalewski,  of  papers  in  the  Ada  Eruditorum  of  1684, 
1691,  1693,  1694,  1702  and  1703;  and  the  Miscellanea 
Berolinensia,  in  No.  162  of  Ostw aid's  Klassiker. 

IV 

THE  CONTROVERSY 

See,  in  the  first  place,  Cantor,  vol.  iii,  pp.  285-328; 
Rosenberger,  pp.  423,  460-506.  Various  letters,  from 
1714-1719,  on  the  controversy  are  mentioned  in  Edleston, 
pp.  xxxviii-xxxix  (see  also  the  notes  referred  to).  An 

1  Archiv  der  Mathematik  und  Physik,  vol.  xxvii,  1856,  pp.  125-132. 

2  Zeitschrift  fur  Mathematik  und  Physik,  vol.  i,  1856,  pp.  240-244. 


NEWTON  AND   LEIBNIZ  115 

account  of  the  controversy,  from  the  point  of  view  of  a 
partisan  of  Newton,  is  given  in  Brewster,  vol.  ii,  pp.  23- 
83 ;  and,  from  this  point  of  view,  reference  may  be  made 
to  H.  Sloman's  book,  The  Claims  of  Leibniz  to  the 
Invention  of  the  Differential  Calculus,  translated  from  the 
German,  with  considerable  additions  and  new  addenda  by 
the  author,  Cambridge,  1860  (cf.  also  Gray,  p.  55). J  On 
the  editions  of  the  Commercium  Epistolicum,  and  so  on, 
see  Gray,  pp.  49~52>  r>  2~3- 

1  With  reference  to  this  book,  it  must  be  remarked  that  Gerhardt 
(cf.  Biv.  1899,  p.  25)  found  that  Leibniz  first  saw,  and  made  extracts 
from,  Newton's  Analysis  in  1676. 


Ill 

REVIEW  (1855)  OF  BREWSTER'S 
"MEMOIRS  OF  NEWTON" 


REVIEW    (1855)    OF    BREWSTER'S 
"MEMOIRS    OF    NEWTON" 

Memoirs  of  the  Life,    Writings,  and  Discoveries  of 
Sir  Isaac   Newton.      By  Sir   David  Brewster, 
K.  H.  ,  etc.  ,  etc.     Two  volumes,  8vo.     Constable 
&  Co.,  Edinburgh, 


I 

NOTHING  is  more  difficult  than  to  settle  who  is  the 
most  illustrious,  the  most  to  be  admired,  in  any 
walk  of  human  greatness.  Those  who  would  brain 
us  —  if  they  could  but  imagine  us  to  have  any  brains 
—  for  hinting  that  it  may  be  a  question  whether 
Shakspere  be  the  first  of  poets,  would  perhaps 
have  been  Homerites  a  century  ago.  In  these 
disputes  there  is  more  than  matter  of  opinion,  or  of 
taste,  or  of  period  :  there  is  also  matter  of  quantity, 
question  of  how  much,  without  any  possibility  of 
bringing  the  thing  to  trial  by  scale.  This  element 
of  difficulty  is  well  illustrated  by  an  exception. 
Among  inquirers  into  what  our  ignorance  calls  the 

1  [On  this  book,  see  note  I  on  p.  3  ;   and,  on  the  subject  of  this 
review,  see  the  Preface.] 

119 


120          REVIEW  OF  BREWSTERyS 

"laws  of  nature,"  an  undisputed  pre-eminence  is 
given  to  Isaac  Newton,  as  well  by  the  popular  voice, 
as  by  the  deliberate  suffrage  of  his  peers.  The 
right  to  this  supremacy  is  almost  demonstrable.  It 
would  be  difficult  to  award  the  palm  to  the  swiftest, 
except  by  set  trial,  with  one  starting-place  and  one 
goal :  nor  could  we  easily  determine  the  strongest 
among  the  strong,  if  the  weights  they  lifted  were  of 
miscellaneous  material  and  bulk.  But  if  we  saw 
one  of  the  swiftest  among  the  runners  keep  ahead 
of  nearly  all  his  comrades,  with  one  of  the  heaviest  of 
the  weights  upon  his  shoulders,  we  should  certainly 
place  him  above  all  his  rivals,  whether  in  activity 
alone,  or  in  strength  alone.  Though  Achilles  were 
the  swifter,  and  Hercules  the  stronger,  a  good 
second  to  both  would  be  placed  above  either.  This 
is  a  statement  of  Newton's  case.  We  cannot  say 
whether  or  no  he  be  the  first  of  mathematicians, 
though  we  should  listen  with  a  feeling  of  possibility 
of  conviction  to  those  who  maintain  the  affirmative. 
We  cannot  pronounce  him  superior  to  all  men  in  the 
sagacity  which  guides  the  observer  of — we  mean 
rather  deducer  from — natural  phenomena,  though 
we  should  be  curious  to  see  what  name  any  six 
competent  jurors  would  unanimously  return  before 
his.  But  we  know  that,  in  the  union  of  the  two 
powers,  the  world  has  never  seen  a  man  comparable 
to  him,  unless  it  be  one  in  whose  case  remoteness  of 
circumstances  creates  great  difficulty  of  comparison. 


"  MEMOIRS    OF  NEWTON"          121 

Far  be  it  from  us  to  say  that  if  Newton  had  been 
Caenopolis,  a  Sicilian  Greek,  he  would  have  sur- 
passed Archimedes  ;  or  that  if  Archimedes  had  been 
Professor  Firstrede,  of  Trinity  College,  Cambridge,  he 
would  have  been  below  Newton,  The  Syracusan  is, 
among  the  ancients,  the  counterpart  of  the  English- 
man among  the  moderns.  Archimedes  is  perhaps 
the  first  among  the  geometers  :  and  he  stands  alone 
in  ancient  physics.  He  gave  a  new  geometry — the 
name  was  afterwards  applied  to  the  infinitesimal 
calculus — out  of  which  he  or  a  successor  would  soon 
have  evolved  an  infinitesimal  calculus,  if  algebra 
had  been  known  in  the  West.  He  founded  the 
sciences  of  statics  and  hydrostatics,  and  we  cannot 
learn  that  any  hint  of  application  of  geometry  to 
physics  had  previously  been  given.  No  Cavalieri, 
no  Fermat,  no  Wallis,  went  before  him  in  geometry  : 
there  was  not  even  a  chance  of  a  contemporary 
Leibniz.  We  cannot  decide  between  Archimedes 
and  Newton  :  the  two  form  a  class  by  themselves 
into  which  no  third  name  can  be  admitted  ;  and  the 
characteristic  of  that  class  is  the  union,  in  most 
unusual  quantity,  of  two  kinds  of  power  not  only 
distinct,  but  so  distinct  that  either  has  often  been 
supposed  to  be  injurious  to  the  favourable  develop- 
ment of  the  other. 

The  scientific  fame  of  Newton,  the  power  which 
he  established  over  his  contemporaries,  and  his  own 
general  high  character,  gave  birth  to  the  desirable 


122       '   REVIEW  OF  BREWS  TER'S 

myth  that  his  goodness  was  paralleled  only  by  his 
intellect.  That  unvarying  dignity  of  mind  is  the 
necessary  concomitant  of  great  power  of  thought, 
is  a  pleasant  creed,  but  hardly  attainable  except  by 
those  whose  love  for  their  faith  is  insured  by  their 
capacity  for  believing  what  they  like.  The  hero  is 
all  hero,  even  to  those  who  would  be  loath  to  pay 
the  compliment  of  perfect  imitation.  Pericles,  no 
doubt,  thought  very  little  of  Hector  dragged  in  the 
dust  behind  the  chariot :  and  Atticus  we  can  easily 
suppose  to  have  found  some  three-quarter  excuse  for 
Romulus  when  he  buried  his  sword  in  his  brother's 
body  by  way  of  enforcing  a  retort.  The  dubious 
actions  of  Newton,  certainly  less  striking  than  those 
of  the  heroes  of  antiquity,  have  found  the  various 
gradations  of  suppressors,  extenuators,  defenders,  and 
admirers.  But  we  live,  not  merely  in  sceptical  days, 
which  doubt  of  Troy  and  will  none  of  Romulus,  but 
in  discriminating  days,  which  insist  on  the  distinc- 
tion between  intellect  and  morals.  Our  generation, 
with  no  lack  of  idols  of  its  own,  has  rudely  invaded 
the  temples  in  which  science  worships  its  founders  : 
and  we  have  before  us  a  biographer  who  feels  that 
he  must  abandon  the  demigod,  and  admit  the  im- 
pugners  of  the  man  to  argument  without  one  cry  of 
blasphemy.  To  do  him  justice,  he  is  more  under  the 
influence  of  his  time,  than  under  its  fear  :  but  very 
great  is  the  difference  between  the  writer  of  the 
present  volumes  and  that  of  the  shorter  Life  in  the 


"MEMOIRS    OF  NEWTON"          123 

"  Family  Library"  in  1831  ;  though,  if  there  be  any 
truth  in  metaphysics,  they  are  the  same  person. 

The  two  deans  of  optical  science,  in  Britain  and 
in  France,  Sir  David  Brewster  and  M.  Biot,  are 
both  biographers  of  Newton,  and  take  rather  different 
sides  on  disputed  points.  Sir  D.  Brewster  was  the 
first  writer  on  optics  in  whose  works  we  took  an 
interest  ;  but  we  do  not  mean  printed  works.  We, 
plural  as  we  are,  remember  well  the  afternoon,  we 
should  say  the  half-holiday,  when  the  kaleidoscope 
which  our  ludi-magister — most  aptly  named  for  that 
term — had  just  received  from  London  was  confided 
to  our  care.  We  remember  the  committee  of  con- 
servation, and  the  regulation  that  each  boy  should, 
at  the  first  round,  have  the  uninterrupted  enjoyment 
of  the  treasure  for  three  minutes  ;  and  we  remember, 
further,  that  we  never  could  have  believed  it  took  so 
very  short  a  time  to  boil  an  egg.  A  fig  for  Jupiter 
and  his  satellites,  and  their  inhabitants  too,  if  any  ! 
What  should  we  have  thought  of  Galileo,  when 
placed  by  the  side  of  the  inventor  of  this  wonder  of 
wonders,  who  had  not  only  made  his  own  telescope, 
but  his  own  starry  firmament  ?  The  inventor  of  the 
kaleidoscope  must  have  passed  the  term  allotted  to 
man,  before  he  put  his  hand  to  the  actual  concoction 
of  these  long-meditated  volumes,  in  which  we  find 
the  only  life  of  Newton  written  on  a  scale  com- 
mensurate with  Newton's  fame.  But  though  he  has 
passed  the  term,  he  has  not  incurred  the  penalty  ; 


124          REVIEW  OF  BREWS  TER'S 

his  strength  is  labour  without  sorrow.  We  trust 
therefore  that  the  still  later  age,  the  full  fourscore, 
will  find  him  in  the  enjoyment  of  the  additional  fame 
which  he  has  so  well  earned.  And  since  his  own 
scientific  sensibilities  are  keen,  as  evidenced  by 
many  a  protest  against  what  he  conceives  to  be 
general  neglect  on  the  part  of  ruling  powers,  we 
hope  they  will  make  him  fully  feel  that  he  has  linked 
his  own  name  to  that  of  his  first  object  of  human 
reverence  for  as  long  as  our  century  shall  retain  a 
place  in  literary  history.  This  will  be  conceded  by 
all,  how  much  soever  they  may  differ  from  the 
author  in  opinions  or  conclusions  ;  and  though  we 
shall  proceed  to  attack  several  of  Sir  D.  Brewster's 
positions,  and  though  we  have  no  hesitation  in 
affirming  that  he  is  still  too  much  of  a  biographer, 
and  too  little  of  an  historian,  we  admire  his  earnest 
enthusiasm,  and  feel  as  strongly  as  any  one  of  his 
assentients  the  service  he  has  rendered  to  our 
literature.  When  a  century  or  two  shall  have 
passed,  we  predict  it  will  be  said  of  our  day 
that  the  time  was  not  come  when  both  sides  of  the 
social  character  of  Newton  could  be  trusted  to  his 
follower  in  experimental  science.  Though  biography 
be  no  longer  an  act  of  worship,  it  is  not  yet  a 
solemn  and  impartial  judgment  :  we  are  in  the  inter- 
mediate stage,  in  which  advocacy  is  the  aim,  and  in 
which  the  biographer,  when  a  thought  more  candid 
than  usual,  avows  that  he  is  to  do  his  best  for  his 


"MEMOIRS    OF  NEWTON"          125 

client.  We  accept  the  book  as  we  find  it ;  we 
expect  an  ex  parte  statement,  and  we  have  it. 
The  minor  offence  is  sometimes  admitted,  with  what 
we  should  call  the  art  of  an  able  counsel,  if  we  did 
not  know  that  the  system  of  the  advocate  in  court  is 
but  the  imitation  of  all  that  is  really  telling  in  the 
natural  practices  of  the  partisan  defender.  But  Sir 
D.  Brewster  stands  clear  of  the  imputation  of  art 
by  the  mixture  of  all  which  art  would  avoid.  A 
judicious  barrister,  when  he  has  to  admit  some 
human  nature  in  his  client,  puts  an  additional  trump 
upon  the  trick  by  making  some  allowance  for  the 
other  side  ;  and  nothing  puts  the  other  side  in  so 
perilous  a  predicament.  It  is  not  so  with  Sir  D. 
Brewster.  When  sins  against  Newton  are  to  be 
punished,  we  hear  Juvenal ;  when  Newton  is  to  be 
reprimanded,  we  hear  a  nice  and  delicate  Horace, 
who  can 

"  In  reverend  bishops  note  some  small  defects ; 
And  own  the  Spaniard  did  a  waggish  thing, 
Who  cropt  our  ears,  and  sent  them  to  the  king." 

We  have  more  reasons  than  one  for  desiring  that  it 
should  have  been  so,  and  not  otherwise.  Sir  D. 
Brewster  is  the  first  biographer  who  has  had  re- 
stricted access  to  the  "  Portsmouth  Papers  "  ;  he  has 
been  allowed  to  have  this  collection  in  his  own 
possession.  Had  the  first  Life  written  upon  know- 
ledge of  these  papers  taken  that  view  of  Newton's 
social  conduct  which  stern  justice  to  others  requires, 


126          REVIEW  OF  BREWSTERS 

a  condonation  of  all  the  previous  offences  of 
biographers  would  have  followed.  There  was  not 
full  information ;  the  fault  lay  with  those  who 
suppressed  the  truth  ;  and  so  forth.  And  every 
great  man  who  has  left  no  hoard  of  papers  would 
have  had  a  seal  of  approval  placed  upon  all  his 
biographies  ;  for,  you  see,  Newton  was  exposed  by 
the  publication  of  the  "  Portsmouth  Papers,"  that  is 
easily  understood  ;  but  A  B  left  no  papers,  there- 
fore no  such  exposure  can  take  place,  etc.,  etc. 
We,  who  hold  that  there  is,  and  long  has  been, 
ample  means  of  proving  the  injustice  with  which 
Newton  and  his  contemporaries  once  and  again 
treated  all  who  did  not  bow  to  the  idol,  should  have 
been  loath  to  see  the  garrison  which  our  opponents 
have  placed  in  the  contested  forts  march  out  with 
the  honours  of  war,  under  a  convention  made  on 
distant  ground,  and  on  a  newly-discovered  basis  of 
treaty.  Again,  there  is  a  convenient  continuity  in 
the  first  disclosure  of  these  documents  coming  from 
an  advocate  ;  the  discussion  which  they  excite  will 
be  better  understood  when  the  defender  of  Newton  is 
the  first  to  have  recourse  to  Newton's  own  papers. 


II 

Of  Newton's  birth,  of  his  father's  death,  and  the 
subsequent  marriage  of  his  mother,  we  need  say 
nothing.  He  was  not  born  with  a  title,  though 


"MEMOIRS    OF  NEWTON"          127 

he  was  the  son  of  a  lord  of  a  very  little  manor,  a 
yeoman's  plot  of  land  with  a  baronial  name.  But 
the  knighthood  clings  strongly  to  his  memory.  Sir 
David  (and  on  looking  back,  we  see  that  the  doctor 
did  just  the  same)  seldom  neglects  it.  When  the 
school-boy  received  a  kick  from  a  school-fellow,  it 
was  "  Sir  Isaac"  who  fought  him  in  the  churchyard, 
and  it  was  <(  Sir  Isaac"  who  rubbed  his  antagonist's 
nose  against  the  wall  in  sign  of  victory.1  Should 
we  survive  Sir  David,  we  shall  Brewster  him  :  we 
hold  that  those  who  are  gone,  when  of  a  certain 
note,  are  entitled  to  the  compliment  of  the  simplest 
nomenclature.  The  childhood  and  boyhood  of 
Newton  were  distinguished  only  by  great  skill  in 
mechanical  contrivance.  No  tradition,  no  remain- 
ing record,  imputes  any  very  early  progress  either 
in  mathematics  or  general  learning,  beyond  what 
is  seen  in  thousands  of  clever  boys  in  any  one  year 
of  the  world.  That  he  was  taken  from  farming 
occupations,  and  sent  back  to  school,  because  he 
loved  study,  is  told  us  in  general  terms  ;  but  what 
study  we  are  not  told.  We  have  always  been  of 
opinion  that  the  diversion  of  Newton's  flow  of  reason 
into  its  proper  channel  was  the  work  of  the  University 
and  its  discipline.  He  was  placed  at  Trinity  College 
as  a  subsizar  in  his  nineteenth  year.  We  have  no 
proof,  but  rather  the  contrary,  that  he  had  then 
opened  Euclid.  That  he  was  caught  solving  a 

1  [C/.  Brewster,  Memoirs^  1855,  vol.  i,  pp.  7-8.] 


128          REVIEW  OF  BREWS  TER'S 

problem  under  a  hedge  is  recorded  :  perhaps  a  knotty 
question  of  wheelwork.  He  bought  a  Euclid  at 
Cambridge,  and  threw  it  aside  as  a  trifling  book, 
because  the  conclusions  were  so  evident :  he  betook 
himself  to  Descartes,  and  afterwards  lamented  that 
he  had  not  given  proper  attention  to  Euclid.  All 
this  is  written,  and  Sir  David  is  bound  to  give  it ; 
but  what  Newton  has  written  belies  it.  We  put 
faith  in  the  Principia,  which  is  the  work  of  an  in- 
ordinate Euclidian,  constantly  attempting  to  clothe 
in  the  forms  of  ancient  geometry  methods  of  pro- 
ceeding which  would  more  easily  have  been  pre- 
sented by  help  of  algebra.  Shall  we  ever  be  told 
that  Bacon  complained  of  the  baldness  of  his  own 
style,  and  wished  he  had  obtained  command  over 
metaphor?  Shall  we  learn  that  Cobbett  lamented 
his  constant  flow  of  Gallicism  and  west-end  slang, 
and  regretted  that  his  English  had  not  been  more 
Saxon  ?  If  we  do,  we  shall  have  three  very  good 
stories  instead  of  one.  We  may  presume  as  not 
unlikely,  that  Newton,  untrained  to  any  science, 
threw  away  his  Euclid  at  first,  as  very  evident :  no 
one  need  be  Newton  to  feel  the  obvious  premise,  or 
to  draw  the  unwise  conclusion.  But  it  would  belong 
to  his  tutor  to  make  him  know  better  :  and  Newton 
was  made,  as  we  shall  see,  to  know  better  accord- 
ingly. Our  reader  must  not  imagine  that  deep 
philosophy  and  high  discovery  were  discernible  in 
the  young  subsizar.  He  was,  as  to  what  had  come 


"MEMOIRS    OF  NEWTON"          129 

out,  a  clever  and  somewhat  self-willed  lad,  rather 
late  at  school,  with  his  heart  in  the  keeping  of  a 
young  lady  who  lived  in  the  house  where  he  had 
boarded,  and  vice  versa,  more  than  commonly  in- 
genious in  the  construction  of  models,  with  a  good 
notion  of  a  comet  as  a  thing  which  might  be  imitated, 
to  the  terror  of  a  rustic  neighbourhood,  by  a  lantern 
in  a  kite's  tail,  and  with  a  tidy  and  more  than  boyish 
notion  of  an  experiment,  as  proved  by  his  making 
an  anemometer  of  himself  by  trial  of  jumping  with 
and  against  the  wind.  In  that  tremendous  storm 
in  which  many  believed  that  Oliver  Cromwell's 
reputed  patron  came  to  carry  him  away,  and  in 
which  he  certainly  died,  the  immortal  author  of  the 
theory  of  gravitation  was  measuring  he  little  knew 
what,  by  jumping  to  and  fro.  We  do  not  desire  to 
see  boys  take  investiture  of  greatness  from  their 
earliest  playtime  :  we  like  to  watch  the  veneration 
of  a  biographer  growing  with  its  cause,  and  the 
attraction  varying  with  some  inverse  power  of  the 
distance.  And  further,  we  are  rather  pleased  to 
find  that  Newton  was  what  mammas  call  a  great  boy 
before  he  was  a  great  man. 

Of  all  the  books  which  Newton  read  before  he 
went  to  Cambridge,  only  one  is  mentioned — Sander- 
son's Logic  :  this  he  studied  so  thoroughly  that  when 
he  came  to  college  lectures  he  was  found  to  know  it 
better  than  his  tutor.  The  work  is,  for  its  size,  un- 
usually rich  in  the  scholastic  distinctions  and  the 

9 


130          REVIEW  OF  BREWSTERS 

parva  logicalia  ;  very  good  food  for  thought  to  those 
who  can  sound  the  depths.  Newton's  Cambridge 
successors  are  apt  to  defend  their  neglect  of  logic 
by  citing  his  supposed  example,  and  that  of  other 
great  men  :  but  it  now  appears  that  Newton  was  not 
only  conversant  with  Barbara,  Celarent,  etc.,  but 
even  with  Fecana,  Cajeti,  Dafenes,  Hebare,  Gadaco, 
etc.  We  have  often  remarked  that  Newton,  as  in 
the  terminal  scholium  of  the  Principia,  had  more 
acquaintance  with  the-  mode  of  thought  of  the 
schoolmen  than  any  ordinary  account  of  his  early 
reading  would  suffice  to  explain.  We  strongly 
suspect  that  he  made  further  incursions  into  the 
old  philosophy,  and  brought  away  the  idea  of 
fluxions,  which  had  been  written  on,  though  not 
in  mathematical  form,  nor  under  that  name. 
Suisset's  tract  on  intension  and  remission  is  fluxional, 
though  not  mathematical  :  in  the  very  first  para- 
graph he  says  that  the  word  "intension"  is  used 
"uno  modo  pro  alteratione  mediante  qua  qualitas 
acquiritur  :  et  sic  loquendo  intensio  est  motus. " 
For  "qualitas"  read  "quantitas,"  and  we  are  as 
near  to  Newton's  idea  as  we  can  well  be. 

In  less  than  four  years  from  the  time  concerning 
which  we  have  presumed  to  ridicule  the  joint 
attempt  of  Conduitt  and  the  biographers  to  create 
a  dawn  for  which  there  is  no  evidence,  the  sun  rose 
indeed.  Shortly  after  Newton  took  his  B.A. 
degree,  in  1665,  he  was  engaged  on  his  discovery 


"  MEMOIRS    OF  NEWTON"          131 

of  fluxions  :  but  there  is  neither  record  nor  tradition 
of  his  having  taken  his  degree  with  any  unusual 
distinction.  Conduitt's  information  on  this  period 
must  be  absurdly  wrong  in  its  dates.  We  are  to 
believe  that  the  young  investigator  who  conceived 
fluxions  in  May  1665,  was,  at  some  time  in  1664, 
found  wanting  in  geometry  by  Barrow,  and  thereby 
led  not  only  to  study  Euclid  more  attentively,  but 
to  ' '  form  a  more  favourable  estimate  of  the  ancient 
geometer  when  he  came  to  the  interesting  proposi- 
tions on  the  equality  of  parallelograms.  ..."  And 
this  when  he  was  deep  in  Descartes's  geometry  of 
co-ordinates.  We  entertain  no  doubt  that  the  un- 
wise contempt  for  demonstration  of  evident  things, 
so  often  cited  as  a  proof  of  great  genius,  and  its 
correction  by  Barrow,  all  took  place  in  the  first  few 
months  of  his  residence  at  Cambridge.1  His  copy 
of  Descartes,  yet  existing,  is  marked  in  various 
places,  "  Error,  error,  non  est  Geom."2  No  such 
phrase  as  "non  est  Geometria "  would  have  been 
used,  except  by  one  who  had  not  only  read  Euclid, 
but  had  contracted  some  of  that  bias  in  favour  of 
Greek  geometry  which  is  afterwards  so  manifest  in 
the  Principia.  Pemberton,  who  speaks  from  com- 
munication with  Newton,  and  is  a  better  authority 
than  Conduitt,  tells  us  that  Newton  regretted  he 
had  not  paid  more  attention  to  Euclid.  And  Doctor 

1  \Cf.   note  I  on  pp.  9-10,   and    Brewster,  Memoirs^  1855,   vol.  i/ 
pp.  21-22,  24.] 

2  [Brewster,  Memoirs,  1855,  vol.  i,  p.  22,  note.] 


132          REVIEW  OF  BREWSTERS 

Sangrado,  when  the  patient  died,  regretted  that  he 
had  not  prescribed  more  bleeding  and  warm  water. 
The  Principia  bears  already  abundant  marks  of 
inordinate  attachment  to  the  ancient  geometry  ;  in 
one  sense,  it  has  died  in  consequence.  If  Newton 
had  followed  his  own  path  of  invention,  and  written 
it  in  fluxions,  the  young  student  of  modern  analysis 
could  have  read  it  to  this  day,  and  would  have  read 
it  with  interest  :  ass  it  is,  he  reads  but  a  section  or 
two,  and  this  only  in  England.  Before  1669,  the 
year  of  his  appointment  to  the  Lucasian  chair,  all 
Newton's  discoveries  had  germed  in  his  mind.  The 
details  are  notorious,  and  Sir  D.  Brewster  is  able 
to  add  a  remarkable  early  paper  on  fluxions  to  those 
already  before  the  world.1 

We  here  come  upon  the  well-known  letter  to  Mr 
Aston,  a  young  man  about  to  travel,  which,  as  Sir 
David  says,  "  throws  a  strong  light  on  the  charac- 
ter and  opinions  of  its  author."  It  does  indeed, 
and  we  greatly  regret  that  the  mode  in  which  that 
character  has  been  represented  as  the  perfection  of 
high-mindedness  compels  us  to  examine  this  early 
exhibition  of  it,  in  connexion  with  one  of  a  later 
date.  Newton  is  advising  his  young  friend  how  to 
act  if  he  should  be  insulted.  Does  he  recommend 
him,  as  a  Christian  man,  to  entertain  no  thought  of 
revenge,  and  to  fear  his  own  conscience  more  than 
the  contempt  of  others  ?  Or,  as  a  rational  man, 

1  [See  the  Appendix  to  the  second  Essay,  above.  ] 


"MEMOIRS   OF  NEWTON"          133 

does  he  dissuade  him  from  the  folly  of  submitting 
the  decision  of  his  difference  to  the  logic  of  sword  or 
pistol  ?  Or,  supposing  him  satisfied  by  well-known 
sophisms  that  the  duel  is  noble  and  necessary,  does 
he  advise  his  friend  to  remember  that  dishonour  is 
dishonour  everywhere  ?  He  writes  as  follows  : — 

"If  you  be  affronted,  it  is  better,  in  a  forraine 
country,  to  pass  it  by  in  silence,  and  with  a  jest, 
though  with  some  dishonour,  than  to  endeavour 
revenge  ;  for,  in  the  first  case,  your  credit's  ne'er  the 
worse  when  you  return  into  England,  or  come  into 
other  company  that  have  not  heard  of  the  quarrell. 
But,  in  the  second  case,  you  may  beare  the  marks 
of  the  quarrell  while  you  live,  if  you  outlive  it  at  all. " 

This  letter  has  often  been  printed,  in  proof  of 
Newton's  sagacity  and  wisdom.  If  Pepys  or 
Boswell  had  written  the  preceding  advice,  they 
would  not  have  been  let  off  very  easily.  Again, 
when,  many  years  after,  Newton  wrote,  as  member 
for  the  University  in  the  Parliament  which  dethroned 
King  James,  to  Dr  Covel  the  Vice-Chancellor,  he 
requests  a  reasonable  decorum  in  proclaiming 
William  and  Mary,  "because,"  says  he,  "  I  hold 
it  to  be  their  interest  to  set  the  best  face  upon 
things,  after  the  example  of  the  London  divines." 
And  again,  "Those  at  Cambridge  ought  not  to 
judge  and  censure  their  superiors,  but  to  obey  and 
honour  them,  according  to  the  law  and  the'  doctrine 
of  passive  obedience."  What  had  Newton  and 
passive  obedience  just  been  doing  with  King  James  ? 


134          REVIEW  OF  BREWS  TER'S 

These  instances,  apart  from  science,  show  us  the 
character  of  Newton  out  of  science  :  he  had  not 
within  himself  the  source  from  whence  to  inculcate 
high  and  true  motives  of  action  upon  others  ;  the 
fear  of  man  was  before  his  eyes.1  But  his  mind 
had  been  represented  as  little  short  of  godlike  :  and 
we  are  forced  upon  proof  of  the  contrary.  Had  it 
been  otherwise,  had  his  defects  been  duly  admitted, 
it  would  have  been  pleasant  to  turn  to  his  uncom- 
promising philosophic  writings,  and  to  the  manner 
in  which,  when  occupied  with  the  distinction  be- 
tween scientific  truth  and  falsehood,  no  meaner 
distinction  ever  arose  in  his  mind.  This  would 
have  been,  but  for  his  worshippers,  our  chief  con- 
cern with  him.  The  time  will  come  when  his  social 
weaknesses  are  only  quoted  in  proof  of  the  com- 
pleteness with  which  a  high  feeling  may  rule  the 
principal  occupation  of  life,  which  has  a  much  slighter 
power  over  the  subordinate  ones.  Strange  as  it 
may  seem,  there  have  been  lawyers  who  have  been 
honest  in  their  practice,  and  otherwise  out  of  it  : 
there  have  been  physicians  who  have  shown  human- 
ity and  kindness,  such  as  no  fee  could  ever  buy,  at 
the  bedside  of  the  patient  and  nowhere  else. 

Ill 

Sir    David    Brewster    gives    Newton's    career    in 
optics  at  great  length  ;  it  is  his  own  subject,   and 

1  [The   letter   to  Aston    is    given,    with    comments,    in   Brewster's 
Memoirs,  1855,  vol.  i,  pp.  34,  385-389.] 


"MEMOIRS    OF  NEWTON"          135 

he  makes  us  feel  how  completely  he  is  at  home. 
He  gives  a  cursory  glance  at  the  science  even  down 
to  our  own  time ;  and  he  does  the  same  with 
astronomy.  The  writer  would  rather  have  had 
more  of  the  time  of  Newton,  and  particularly,  more 
extracts  from  the  "  Portsmouth  Papers."  But  we 
must  think  of  our  neighbours  as  well  as  of  our- 
selves ;  and  the  general  reader  will  be  glad  to  know 
that  so  much  of  the  work  is  especially  intended  for 
him.  We  have  not  space  to  write  an  abstract  ; 
but  the  book  is  very  readable.  In  the  turmoil  of 
discussion  which  arose  out  of  his  optical  announce- 
ments, Newton  made  the  resolution,  which  he 
never  willingly  broke,  of  continuing  his  researches 
only  for  his  own  private  satisfaction.  I  see,  said 
he,  that  a  man  must  either  resolve  to  put  out 
nothing  new,  or  to  become  a  slave  to  defend  it.  It 
seems  that  he  expected  all  his  discoveries  to  be 
received  without  opposition. 

About  1670,  or  later,  Newton  drew  up  a  scheme 
for  management  of  the  Royal  Society,  which  Sir 
D.  Brewster  found  among  the  papers.  Certain 
members,  some  in  each  department,  should  be  paid, 
and  should  have  fixed  duties  in  the  examination 
of  books,  papers,  experiments,  etc.  In  this  paper 
our  writer,  whose  views  on  this  subject  are  very 
large  and  of  old  standing,  sees  the  recommendation 
of  an  Institute,  which  indeed,  on  a  small  scale,  the 
plan  seems  to  advocate.  Sir  David  would  have  all 


136          REVIEW  OF  BREWSTERS 

the  societies  congregated  at  Kensington  Gore,  under 
liberal  patronage,  and  images  to  himself  that 
*  *  each  member  of  the  now  insulated  Societies  would 
listen  to  the  memoirs  and  discussions  of  the  as- 
sembled Academy,1  and  science  and  literature  would 
thus  receive  a  new  impulse  from  the  number  and 
.  variety  of  their  worshippers  ! "  If  all  Fellows  were 
savants,  and  if  all  savants  studied  all  sciences,  this 
might  be  practicable.  There  is  one  body  in  London 
which  cultivates  a  large  range  of  subjects,  the  Royal 
Society  itself:  and  all  the  world  knows  that  the 
meetings  of  this  Society,  abounding  in  Fellows  of 
such  universality  of  knowledge  as  in  our  time  is 
practicable,  are  less  interesting  and  worse  attended 
than  those  of  any  of  the  societies  for  special  objects. 
And  reason  good  :  the  astronomer  or  the  geologist 
goes  down  to  his  own  place  for  he  knows  what ; 
but  the  astronomer  is  shy  of  a  society  of  which  it 
is  as  likely  that  any  one  evening  may  give  him  a 
treat  of  physiology  as  of  astronomy,  and  the 
geologist,  who  wants  a  stone  when  he  asks  for 
bread,  turns  very  sleepy  under  a  dose  of  hyper- 
determinants  or  definite  integrals. 

Newton's  reputation    rests  on  a  tripod,   the  feet 

1  The  members  of  the  French  Institute  receive  a  part  of  their 
emoluments  at  the  Board,  and  the  quotum  of  each  day  on  which  any 
one  is  absent  is  forfeited.  This  insures  good  attendance,  and  we  have, 
on  pay-day,  seen  men  of  profound  science,  during  the  memoirs  and 
discussions  of  the  assembled  Academy,  practising  the  first  rule  of 
arithmetic,  called  numeration,  upon  rouleaux  of  five-franc  pieces.  To 
this  it  must  be  added  that  the  Institute  has  much  patronage,  and 
constant  attendance  is  necessary  to  keep  up  influence  and  connexion. 


"MEMOIRS   OF  NEWTON"          137 

of  which    are   fluxions,   optics,    gravitation.      Each 
one  of  these  words  must  be  used  in  a  very  large 
sense  :    thus  by  fluxions  we  mean  all  mathematics 
as  bearing  upon  a  system  of  which    the    fluxional 
calculus  is  at  the  completion.      Of  the  three  supports 
of  this  tripod  one  only  has  received  any  damage, 
though  left  quite  strong  enough,  in  conjunction  with 
the  rest,  to  support  the  fabric  through  all  time.      In 
optics  only,  the  subject  on  which  Newton  showed 
his  first  impatience  of  opposition,  his  opinion,  even 
his  system,  has  been  set  aside  in  our  own  day.      The 
hypothesis  of  an  undulating  ether,  as  the  immediate 
agent  in  the  production    of  light,    has    superseded 
that  of  particles  emanating  from  the  luminous  body  : 
and  though  the  undulationists,  now  a  large  majority, 
have    long  maintained    their    theory  with  a  higher 
order  of  certainty  than  they  were  entitled  to,  yet 
it  seems  that  time  is  drifting  their  conclusions  to  a 
stable  anchorage.      There  is  something  like  coinci- 
dence in  the  almost  simultaneous  appearance  of  the 
first  elaborate  biography  of  Newton,  who  well-nigh 
strangled  the  undulatory  theory  in  its  cradle,  and 
of  that  of  Young,  who  first  played  a  part  of  power 
in  its  resuscitation.      As  yet,  Young  is  fully  known 
but  to  a  few  :  his  early  education  was  not,  like  that 
of  Newton,  conducted  under  a  system  which  corrects 
the  false  impressions  of  green  age.      Had  he  been 
trained   in   a   University,    he  would  have  been,   as 
they  say  of  the  globe,  rectified  for  the  latitude  of 


138          REVIEW  OF  BREWSTERS 

the  place  :  but  speculation  on  what  he  might  have 
become  may  be  deferred  until  what  he  did  become 
is  of  more  popular  notoriety.  Dean  Peacock's  Life 
is  one  of  the  best  of  scientific  biographies,  and  the 
three  volumes  of  Young's  collected  writings  are 
treasures  to  all  who  know  what  intellectual  wealth  is. 


IV 

We  come  to  the  Principia^  and  we  confess  that  we 
heartily  wish  it  were  but  just  and  right  to  persuade 
ourselves  that  the  author  of  this  work  could  do  no 
wrong.  One  of  the  greatest  wonders  about  it  is  the 
manner  in  which  it  was  thrown  off  in  eighteen 
months.  Certainly  the  matter  had  fermented  in 
Newton's  mind  many  years  before  :  but  it  was  not 
the  irresistible  call  of  his  own  genius  which  drew 
him  to  the  work  in  December  1684 ;  it  was  Halley, 
and  the  influence  of  the  Royal  Society  brought  to 
bear  by  Halley.  Sir  D.  Brewster  very  properly 
contends  that  to  Halley,  not  to  the  Society,  the 
Principia  is  due.  Who  found  out,  casually,  that 
Newton  had  had  some  great  success  in  the  question 
which  had  occupied  many  of  the  first  minds,  the 
connexion  of  the  planetary  motions  with  mechanical 
second  causes  ?  Who  went  to  Cambridge  .to  learn 
the  truth  of  the  report,  obtained  specimens  from 
Newton  with  a  promise  to  go  on,  got  himself  ap- 
pointed by  the  Royal  Society  to  c '  keep  Mr  Newton 


"MEMOIRS    OF  NEWTON"          139 

in  mind  of  his  promise,"  did  keep  Mr  Newton  in 
mind,  and  doubtless  let  him  have  no  peace  unless  he 
continually  reported  progress?  Who,  when  Newton, 
disgusted  with  the  unfair  claim  of  Hooke,  proposed 
to  leave  out  the  third  book  (that  is,  all  the  applica- 
tion of  the  previous  books  to  the  actual  solar  system)^ 
soothed  him  with  skilful  kindness,  and  made  what 
Sir  D.  Brewster  calls  his  "excellent  temper"  re- 
cover its  serenity  ?  Who  paid  the  expense  of  print- 
ing, when  the  Royal  Society  found  it  could  not  afford 
to  fulfil  its  engagement  ?  To  all  those  questions  the 
answer  is — Halley,  who  shines  round  the  work,  as 
Newton  shines  in  it.  When  Newton  proposed  to 
leave  out  the  third  book,  he  felt  that  Philosophies 
Naturalis  Principia  Mathematica  was  no  longer  the 
true  title,  but  rather  De  Motu  Corporum  Libri  Duo  ; 
but,  feeling  this,  he  intended  to  preserve  the  wrong 
title,  because,  as  he  says  to  Halley,  "'Twill  help 
the  sale  of  the  book,  which  I  ought  not  to  diminish 
now  'tis  yours."  The  greatest  of  all  works  of  dis- 
covery, with  a  catch-penny  title  !  We  can  hardly 
excuse  this,  even  though  the  penny  were  angled  for 
by  a  feeling  of  gratitude.  We  never  liked  the 
"Erne,  lege,  fruere,"  which  figures  in  the  title-page 
of  Copernicus  :  this  was  the  work  of  an  injudicious 
friend  ;  but  Newton  was  only  saved  from  worse  by 
his  incomparable  adviser. 

We  are  come  to  the  time  when  the  morbid  dislike 
of  opposition  which  would,  but  for  Halley,  first  have 


140          REVIEW  OF  BREWS  TERS 

prevented  the  Principia  from  being  written,  and  next 
have  deprived  it  of  its  essential  conclusions,  is  no 
longer  regarded  as  the  modesty  of  true  greatness, 
and  served  up  for  us  to  admire,  as  we  shall  answer 
the  contrary  at  our  peril.  It  is  passed  without  com- 
ment ;  we  are  now  in  slack  water,  and  the  turn  of 
tide  will  be  here  in  due  season.  The  sooner  the 
better  ;  for  the  indulgence  due  to  the  mother  failings 
of  a  great  public  benefactor  cannot  be  cheerfully 
and  cordially  given  so  long  as  our  gratitude  is  re- 
quired to  show  itself  in  misnomers  and  make-believes. 
Candid  acknowledgment  would  convert  censure  into 
regret  :  sufficient  acknowledgment  would  turn  the 
reader  into  an  extenuator :  the  Principia  would 
neutralise  greater  faults  than  Newton's  ;  but  it  will 
not  convert  them  into  merits.  The  quarrel  is  not 
with  Newton  for  his  weaknesses,  but  with  the 
biographer  for  his  misconception  of  his  own  office. 
How  indeed  would  it  be  possible  to  think  for  a 
moment  with  harshness  of  a  great  man  of  all  time, 
and  a  good  man  of  an  evil  time,  on  account  of 
errors  which  we  never  could  have  known  but  for  the 
benefits  to  ourselves  in  the  achievement  of  which 
they  were  committed  ? 

If  faults  had  exhibited  themselves  in  matters 
affecting  society  at  large,  by  offences,  as  it  were, 
against  the  Crown,  the  fountain  of  justice  would 
also  have  been  that  of  mercy,  and  the  evidence  to 
character  and  services  would  have  secured  a  nominal 


"MEMOIRS    OF  NEWTON"          141 

sentence.  But  the  suits  we  have  to  deal  with  are 
in  civil  process.  The  memory  of  more  than  one 
illustrious  contemporary  brings  an  action  for  damages, 
and  palliation  of  the  defendant  is  injustice  to  the 
plaintiff. 

Though  not  much  relying  on  Conduitt's  memo- 
randa of  mathematical  conversations,  we  trust  that 
which  follows,  and  it  will  much  please  young  mathe- 
maticians to  read  of  Newton  in  one  of  their  own 
scrapes.  When  Halley  visited  him  in  1684, — 

.  .  .  .  * '  he  at  once  indicated  the  object  of  his  visit 
by  asking  Newton  what  would  be  the  curve  described 
by  the  planets  on  the  supposition  that  gravity 
diminished  as  the  square  of  the  distance.  Newton 
immediately  answered,  an  Ellipse.  Struck  with  joy 
and  amazement,  Halley  asked  him  how  he  knew  it  ? 
Why,  replied  he,  I  have  calculated  it ;  and  being 
asked  for  the  calculation,  he  could  not  find  it,  but 
promised  to  send  it  to  him.  After  Halley  left 
Cambridge,  Newton  endeavoured  to  reproduce  the 
calculation,  but  did  not  succeed  in  obtaining  the 
same  result.  Upon  examining  carefully  his  diagram 
and  calculation,  he  found  that  in  describing  an 
ellipse  coarsely  with  his  own  hand,  he  had  drawn  the 
two  axes  of  the  curve  instead  of  two  conjugate 
diameters,  somewhat  inclined  to  one  another. 
When  this  mistake  was  corrected,  he  obtained  the 
result  which  he  had  announced  to  Halley." 

This  anecdote  1  carries  truth  on  the  face  of  it,  for 
Conduitt  was  neither  mathematician  enough  to  have 
conceived  it,  nor  to  have  misconceived  it  into  any- 

1  [Brewster,  Memoirs ^  1855,  vol.  i,  p.  297.] 


H2          REVIEW  OF  BREWS  TERS 

thing  so  natural  and  probable  as  what  he  has  given. 
Little  things  illustrate  great  ones.  Newton,  whose 
sagacity  in  pure  mathematics  has  an  air  of  divina- 
tion, who  has  left  statements  of  results  without 
demonstration,  so  far  advanced  that  to  this  day  we 
cannot  imagine  how  they  were  obtained,  except  by 
attributing  to  him  developments  of  the  doctrine  of 
fluxions  far,  far  beyond  what  he  published,  or  any 
one  of  his  time — this  Newton  was  liable,  both  in 
his  own  closet  and  in  his  printed  page,  to  those  little 
incurite  which  the  man  of  pen  and  ink  must  some- 
times commit,  and  which  the  man  who  can  push 
through  a  mental  process  may  indeed  commit,  but 
is  almost  sure  to  detect  when  he  empties  his  head 
upon  paper.  Now  join  what  precedes  to  Newton's 
own  assertion  that  he  had  no  peculiar  sagacity,  but 
that  all  he  had  done  was  due  to  patience  and  perse- 
verance ;  an  assertion  at  any  common  interpretation 
of  which  we  may  well  smile,  but  which,  all  things 
put  together,  may  justify  us  in  such  an  irreverent 
simile  as  the  supposition  that  he  hunted  rather  by 
scent  than  by  sight. 

V 

We  now  come  to  the  second  volume,  and  to  those 
points  on  which  we  more  especially  differ  from  Sir 
D.  Brewster.  Our  plan  must  be  to  take  one  or  two 
prominent  cases,  and  to  discuss  them  with  the 
biographer.  We  do  not  express  disapprobation  at 


"  MEMOIRS    OF  NEWTON"          143 

the  facility  with  which  he  credits  the  opponents  of 
Newton  with  bad  motives  :  we  are  glad  of  it,  and 
thank  him  for  it.  There  is  a  pledge  of  earnest 
sincerity  in  the  wildness  with  which  the  barbed 
arrow  is  fired  at  Leibniz  or  at  Flamsteed  ;  and  if  the 
partisan  be  too  much  led  away  by  his  feelings  to  be 
a  judicious  counsel,  it  is  not  we,  to  whom  trouble  is 
saved,  who  ought  to  blame  him  for  it.  We  take  the 
following  as  an  instance,  chiefly  because  we  can  be 
brief  upon  it. 

Newton  and  others,  acting  for  Prince  George, 
entered  into  an  agreement  with  Flamsteed  :  articles 
of  agreement  were  signed,  out  of  the  execution  of 
which  quarrels  arose.  We  must  know,  as  Sir  David 
justly  observes,  what  these  articles  were  before  we 
can  judge.  No  signed  copy  appears  :  Mr  Baily 
found  none  among  Flamsteed's  papers,  Sir  David 
found  none  among  Newton's.  But  draught  articles 
occur  in  both  repositories  :  and,  wonderful  to  relate, 
the  unsigned  draughts  actually  differ  ;  Flamsteed's 
draughts  bind  him  less,  Newton's  draughts  bind 
Flamsteed  more.  The  case  is  a  very  common  one  ; 
the  manner  in  which  Sir  David  treats  it  is  not  quite 
so  common.  Speaking  of  Flamsteed,  he  informs  us 
that  ' '  of  these  he  has  left  no  copy,  because  he  had 
wilfully  violated  them  "  :  speaking  of  the  draughts 
in  Newton's  possession,  he  says,  *  *  I  regret  to  say 
that  they  are  essentially  different  from  those 
published  by  Mr.  Baily  "  ;  by  which  he  means  that 


H4          REVIEW  OF  BREWSTERS 

Newton's  unsigned  papers  are  of  course  copies  of 
the  signed  agreement,  and  Flamsteed's  of  course  no 
such  thing  ;  the  false  draughts  being  purposely 
retained  by  Flamsteed,  in  preference  to  the  final 
articles  purposely  destroyed.  We  need  not  tell  our 
readers  that  a  man  is  not  to  be  pronounced  dis- 
honest because  his  draught  proposals  do  not  agree 
with  his  signed  covenants,  still  less  because  they  do 
not  agree  with  the  other  parties'  draught  proposals. 
Newton  and  Flamsteed  were  both  honest  men,  with 
very  marked  faults  of  different  kinds  :  we  may  be 
sure  neither  of  them  privately  destroyed  a  document 
for  the  suppression  of  evidence.  When  Sir  D. 
Brewster  not  merely  opines,  but  narrates,  that 
Flamsteed  left  no  copy  because  he  had  wilfully 
violated  them,  he  is  our  very  good  friend,  and 
lightens  our  task  very  much. 

When  Newton  allowed  himself  to  perpetrate,  not 
the  suppression  of  a  document,  for  a  third  edition 
does  not  suppress  the  first  and  second,  but  a  revoca- 
tion so  made  as  to  do  all  that  could  be  done  towards 
suppression,  Sir  David  Brewster  is  his  defender,  and 
in  this  instance,  we  really  believe,  one  of  the  last  of 
his  defenders.  He  thinks  the  step  was  "perhaps 
unwise,"  but  proceeds  to  say  that  Newton  was  "  not 
only  entitled  but  constrained  "  to  cancel  the  passage. 

When  Leibniz  applied  to  Newton  for  information 
on  the  nature  of  the  discoveries  with  rumours  of 
which  the  English  world  was  ringing,  Newton  com- 


"MEMOIRS    OF  NEWTON"          145 

municated    some    of  his  algebraic    discoveries,   but 
studiously    concealed     a     descriptive    mention     of 
fluxions  under  the  celebrated  anagrams,  or  sentences 
with  their  letters  transposed  into  alphabetical  order. 
Leibniz  (1677)  replied,  almost  immediately,  with  a 
full  and  fair  disclosure  of  his  own  differential  calculus, 
and  in  so  doing  became  the  first  publisher  of  that 
method,  and  under  the  symbols  which  are  now  in 
universal    use.      He  adds  that  he  thinks    Newton's 
concealed    method    must    resemble   his    own  ;    thus 
holding    out    an  invitation    to    Newton    to  say  yes 
or    no.      Not    one  word    of  answer    from    Newton. 
Accordingly,   when    Leibniz    printed    his    discovery 
in  the  Leipsic  Acts  for  1684,  he  did  not  affirm  that 
Newton  was  in  possession  of  a  method  similar  to  his 
own.     What  ought  he  to  have  done,  we  ask  of  our 
readers,  under  these  circumstances  ?     Ought  he  to 
have  given  Newton's  assertions  about  his  method, 
as  assertions,  leaving  it  to  a  suspicious  temper  to 
surmise  that  the  reader  was  desired  not  to  believe 
without  proof?     Ought  he,  as  a  matter  of  compli- 
ment, to  have  promulgated  what  Newton  was  doing 
everything  in  the  power  to  conceal?     Seven  years 
had  passed,  and    Newton  had  made  no  sign  :  was 
Leibniz  bound,  either  in  fairness  or  in  courtesy,  to 
take  on   himself  to  affirm    that   he  had  a  method 
similar  to  his  own  ?     Not  in  fairness  ;  for  if  a  man 
studiously  conceal  and  continue  to  conceal  his  dis- 
covery, those  to  whom  he  may  have  stated  that  he 

10 


146          REVIEW  OF  BREWSTERS 

had  a  discovery  are  not  bound  to  be  his  trumpeters 
until  such  time  as  he  shall  please  to  reveal  himself. 
Not  in  courtesy  ;  a  man  who  sends  only  anagrams, 
and  when  he  receives  from  his  correspondent  a  full 
and  open  account  of  that  correspondent's  discoveries, 
and  an  invitation  to  state  whether  his  own  resemble 
them,  returns  no  answer,  cannot  complain  of  want 
of  courtesy  if  his  correspondent  keep  silence  about 
him  thenceforward.  What  Leibniz  did  was  merely 
to  state  that  no  one  would  successfully  treat  such 
problems  as  he  had  treated,  except  by  his  own 
calculus,  or  one  similar  to  it.  Sir  D.  Brewster  calls 
his  silence  with  respect  to  Newton  the  first  fault  in 
the  controversy  :  we  see  no  fault  at  all ;  and  if  we 
did,  we  should  call  it  the  second.  The  paper  had 
no  historical  allusions  ;  Cavalieri,  Fermat,  and 
Hudde,  each  of  whom  had  shown  the  world  some- 
thing approaching  to  calculus,  are  not  named  in  it  : 
and  either  of  these  had  more  claim  to  mention  than 
Newton  at  that  time.  But,  two  years  afterwards, 
in  1686,  Leibniz  published  a  paper  in  the  same 
Leipsic  Acts,  a  paper  which  Newton  did  not  cite 
when,  long  after,  he  was  writing  against  Leibniz, 
a  paper  which  the  Newtonians  are  very  shy  of 
citing,  and  of  which,  apparently,  Sir  David  knows 
nothing.  In  this  paper  he  explains  the  foundation 
of  the  integral  calculus,  the  matter  of  which  was 
much  more  likely  to  recall  Newton  to  mind  than 
his  former  paper  on  the  differential  calculus  :  for 


"MEMOIRS    OF  NEWTON"          147 

his  application  to  Newton,  in  the  first  instance, 
was  to  know  what  he  had  done  on  series,  and 
especially  with  reference  to  their  use  in  quadratures  > 
which  we  now  call  integration.  Here  he  gives  an 
historical  summary  ;  and  speaking  of  those  who  had 
performed  quadratures  by  series,  he  proceeds  thus  ; 
— "  A  geometer  of  the  most  profound  genius,  Isaac 
Newton,  has  not  only  arrived  at  this  point  inde- 
pendently of  others,  but  has  solved  the  question  by 
a  certain  universal  method  :  and  if  he  would  publish, 
which  I  understand  he  is  now  preparing  to  do, 
beyond  doubt  he  would  open  new  paths,  to  the 
great  increase,  as  well  as  condensation,  of  science. " 
A  passing  word  on  Leibniz.  We  shall  not  stop  to 
investigate  the  various  new  forms  in  which  Sir  D. 
Brewster  tries  to  make  him  out  tricking  and  paltry. 
We  have  gone  through  all  the  stages  which  a  reader 
of  English  works  can  go  through.  We  were  taught, 
even  in  boyhood,  that  the  Royal  Society  had  made 
it  clear  that  Leibniz  stole  his  method  from  Newton. 
By  our  own  unassisted  research  into  original  docu- 
ments we  have  arrived  at  the  conclusion  that  he  was 
honest,  candid,  unsuspecting,  and  benevolent.  His 
life  was  passed  in  law,  diplomacy,  and  public  business  ;  * 
his  leisure  was  occupied  mostly  by  psychology,  and 
in  a  less  degree  by  mathematics.  Into  this  last 
science  he  made  some  incursions,  produced  one  of 
the  greatest  of  its  inventions,  almost  simultaneously 
with  one  of  its  greatest  names,  and  made  himself 


148          REVIEW  OF  BREWSTERS 

what  Sir  D.  Brewster  calls  the  "  great  rival"  of 
Newton,  in  Newton's  most  remarkable  mathematical 
achievement.1 

Newton,  in  the  first  edition  of  the  Principia^ 
gave  a  fair  and  candid  account  of  the  matter.  But, 
many  years  after,  when  this  important  passage 
was  quoted  against  those  (and  we  now  know  that 
Newton  was  always  one  of  them)  who  endeavoured 
to  prove  Leibniz  a  plagiarist,  he  tried  to  explain 
away  the  force  of  his  own  admission.  This  he 
did  twice  ;  once  in  a  private  paper  which  Sir  D. 
Brewster  has  published — and,  strange  to  say,  in 
vindication  of  the  suppression  of  the  passage  which 
took  place  in  the  third  edition — and  once  in  those 
observations  on  Leibniz's  last  letter  which  he  cir- 
culated among  friends  until  Leibniz  died  and  then 
sent  at  once  to  press.  We  give  the  Scholium  from 
the  Principia,  and  the  two  explanations. 

Scholium  from  the  '  '  Principia  "  (first  edition). 
"  In  letters  which  passed  between  me  and  that  most 
skilful  geometer  G.  G.  Leibnitz  ten  years  ago, 
when  I  signified  that  I  had  a  method  of  determining 
maxima  and  minima,  of  drawing  tangents  to  curves, 
and  the  like,  which  would  apply  equally  to  irrational 
as  to  rational  quantities,  and  concealed  it  under  trans- 
posed letters  which  would  form  the  following  sentence 
—  'Data  aequatione  quotcunque  fluentes  quantitates 

1  [De  Morgan  wrote  a  biography  of  Leibniz,  an  extract  from  which  is 
given  in  the  first  Appendix  to  this  Essay.] 


"MEMOIRS   OF  NEWTON" 


149 


involvente,  fluxiones  invenire,  et  vice  versa ' — that 
eminent  man  wrote  back  that  he  had  fallen  upon  a 
method  of  the  same  kind,  and  communicated  his 
method,  which  hardly  differed  from  mine  in  any- 
thing except  language  and  symbols.  The  founda- 
tion of  both  is  contained  in  the  preceding  Lemma. " 


Newton's  explanation^  left 
in  manuscript. 


"After  seven  years,  viz. 
in  October  1684,  he  pub- 
lished the  elements  of  this 
method  as  his  own,  without 
referring  to  the  correspon- 
dence which  he  formerly 
had  with  the  English  about 
these  matters.  ,  He  men- 
tioned indeed,  a  methodus 
similis,  but  whose  that  method 
was,  and  what  he  knew  of  it, 
he  did  not  say,  as  he  should 
have  done.  And  thus  his 
silence  put  me  upon  a  necessity 
of  writing  the  Scholium  upon 
the  second  Lemma  of  the 
second  Book  of  Principles, 
lest  it  should  be  thought  that 
I  borrowed that  Lemma  from 
Mr  Leibnitz," 


Newton's  explanation  circu- 
lated in  writing,  and  printed 
in  Raphson's  "Fluxions" 
(1716,  date  of  title  1715) 
after  Leibniz's  death. 

P.  115.  "He  pretends 
that  in  my  book  of  Principles, 
PP-  2S3>  254>  I  allowed  him 
the  invention  of  the  Calculus 
Differential  independently 
of  my  own  ;  and  that  to  at- 
tribute this  invention  to  my- 
self, is  contrary  to  my  know- 
ledge. But  in  the  paragraph 
there  referred  unto,  I  do  not 
find  one  word  to  this  purpose. 
On  the  contrary,  I  there  re- 
present that  I  sent  notice  of 
my  method  to  Mr  Leibnitz 
before  he  sent  notice  of  his 
method  to  me  :  and  left  him 
to  make  it  appear  that  he 
had  found  his  method  before 
the  date  of  my  letter;  that 
is,  eight  months  at  least 
before  the  date  of  his  own. 
And  by  referring  to  the  letters 
which  passed  between  Mr 
Leibnitz  and  me  ten  years 
before,  I  left  the  reader  to  con- 
sult these  letters,  and  inter- 
pret the  paragraph  thereby." 


150          REVIEW  OF  BREWS  TER'S 

The  first  explanation  is  from  a  manuscript  supple- 
ment to  that  printed  answer  to  Leibniz  of  which 
the  second  explanation  is  part.  We  think  better  of 
Newton  in  1687  than  to  believe  either,  though  we 
do  not  doubt  that  Newton  in  1716  saw  his  former 
self  through  the  clouds  of  1712.  Though  the 
morbid  suspicion  of  others,  which  was  the  worst 
fault  of  temperament,  the  fault  alluded  to  by  Locke, 
did  act  to  some  extent  throughout  his  whole  life, 
yet  we  do  not  believe  that  it  was  in  1687  what  it 
afterwards  became  when  he  had  sat  on  the  throne  of 
science  for  many  years,  the  object  of  every  form  of 
admiration,  and  every  form  of  flattery.  Could  we 
believe  his  first  explanation,  could  we  think  that 
in  1687  his  hidden  anagrams,  answered  by  Leibniz's 
candid  revelations,  produced  no  effect  except  a 
diseased  feeling  that  perhaps  Leibniz  would  rob 
him,  instead  of  a  generous  confidence  that  Leibniz 
would  not  suspect  him,  we  should  turn  from  him 
with  pity.  We  must  now  change  our  position,  and 
defend  him  from  his  biographer.  Sir  D.  Brewster 
does  not  quote  the  second  explanation  ;  he  only 
cites  the  page,  and  quotes  a  few  words  occurring 
further  on,  which  are  much  less  to  the  purpose,  and 
which  he  says  ' '  fortunately "  give  us  Newton's 
opinion.  Now  we  say  that  the  second  explanation, 
as  quoted  by  us,  fortunately  saves  Newton  from 
his  own  imputation  upon  himself.  The  two  ex- 
planations cannot  stand  together  :  according  to  the 


"MEMOIRS    OF  NEWTON"          151 

first  Newton  was  guarding  himself  from  a  charge  of 
plagiarism  ;  according  to  the  second,  he  was  putting 
upon  Leibniz  the  onus  of  averting  a  similar  charge 
from  himself.  Both  motives  might  have  been  simul- 
taneous ;  but  both  could  not  be  so  much  the  chief 
motives  as  to  be  separately  worthy  of  standing  alone. 
But  the  most  precious  inference  in  Newton's  favour  is 
that  the  second  explanation l  is  demonstrably  not  the 
true  one,  and  the  disorder  of  mind  which  perverted 
the  best-known  facts  may  as  easily,  and  more  easily, 
have  perverted  the  memory  of  impressions.  Those 
letters  which  Newton  referred  to  that  the  reader 
might  consult  them,  for  interpretation  of  his  printed 
paragraph,  had  never  been  published,  had  never 
been  announced,  were  not  then  likely  to  be  published, 
and  in  fact  never  were  published  till  1699,  thirteen 

1  In  reference  to  both  explanations,  the  following  is  remarkable. 
Just  after  Leibniz  made  his  publication  of  1684,  a  young  Scotchman, 
Craig,  then  of  Cambridge,  took  it  up,  and  published  a  short  tract  upon 
the  quadrature  of  curves,  in  which  he  uses,  with  high  praise,  the 
differential  calculus  of  Leibniz.  He  had  been  in  communication  with 
Newton,  had  asked  for  help  in  this  very  subject  of  quadrature,  and  had 
received  the  binomial  theorem,  then  unprinted.  But  not  one  word 
did  Newton  drop  to  the  effect  that  he  also  had  a  method  like  that  of 
Leibniz,  and  that  he  and  Leibniz  had  communicated  seven  or  eight 
years  before.  Craig  says,  long  after,  in  1718,  that  Newton  examined 
the  manuscript  :  it  is  clear,  however,  that  his  memory  is  at  fault  here, 
and  that  it  was  the  second  edition  (1693)  which  Newton  examined.  Are 
we  to  believe  that  Newton  was  brooding  over  the  matter  of  the  two 
explanations,  at  a  time  when  he  allowed  his  young  friend  to  proclaim 
Leibniz  as  the  author  of  the  new  calculus,  with  that  negation  of  himself 
which  was  implied  in  acknowledgment  of  assistance  on  another  point '? 
We  rather  suspect  that,  at  the  time,  when  the  geometrical  form  which 
is  so  prominent  in  the  Principia,  then  on  the  anvil,  was  in  his  mind, 
he  greatly  undervalued  his  own  fluxions.  And  we  think  they  never 
would  have  been  heard  of  if  the  mighty  force  which  the  calculus  had 
developed  by  1693  had  not  shown  him  how  much  there  was  to  contend 
for. 


152          REVIEW  OF  BREWS TER'S 

years  afterwards.  Moreover,  the  letters  were  not 
written  by  Leibniz  and  Newton  to  one  another,  but 
by  both  to  Oldenburg  :  how  could  the  readers  of 
the  Principia  have  known  what  to  go  to  ;  or  how 
could  they  have  gone  to  the  letters,  if  they  had 
known  ?  The  truth  we  suspect  to  be  as  follows  : — 
In  1712,  when  those  letters  were  first  republished, 
the  second  edition  of  the  Principia  was  in  preparation, 
and  the  battle  of  fluxions  was  raging  :  we  believe 
that  in  1716,  all  that  Newton  said  of  himself  in 
reference  to  the  first  edition  of  the  Principia  must 
be  referred  to  the  Newton  of  the  second  edition. 
On  any  other  supposition,  except  morbid  confusion 
of  ideas,  Newton  must  be  charged  with  worse  than 
we  ever  believed  of  him.  What  well-read  and 
practised  investigator,  with  his  mind  in  its  normal 
state,  and  all  his  books  before  him,  ever  mistakes 
the  date  of  first  publication  of  any  of  his  own  works 
by  thirteen  years,  in  a  deliberate  answer  to  an 
acute  opponent  ?  Again,  Newton  is  quite  wrong 
as  to  the  eight  months  which  he  gives  Leibniz  to 
execute  his  alleged  fraud  in.  His  own  Commercium 
Epistolicum  would  have  taught  him  better.  Though 
his  second  letter  to  Oldenburg  (the  one  in  question) 
was  dated  October  the  24th,  1676,  and  Leibniz's 
answer  June  the  2ist,  1677,  yet  Collins  informs 
Newton  that  the  copy  intended  for  Leibniz  was  in 
his  hands  on  March  the  5th,  1677,  but  that  in  a  week 
it  would  be  despatched  to  Hanover  by  a  private  hand. 


"  MEMOIRS    OF  NEWTON"          153 

We   are    of  opinion    that    the    moral  intellect  of 
Newton — -not  his  moral  intention,  but  his  power  of 
judging — underwent    a    gradual    deterioration  from 
the  time  when  he  settled  in  London.      We  see  the 
faint  traces  of  it  in  his  manner  of  repudiation  of  the 
infinitesimal  view  of  fluxions,  in   1704.      A  man  of 
sound    judgment    as    to   what    is    right    does    not 
abandon  a  view  which  he  has  held  in  common  with 
a    great    rival,  and    this   just    at    a    time  when  the 
world  is  beginning  to  ask  which  came  first  in  their 
common  discovery,  without  a  clear  admission  of  the 
abandonment  :    he  does  not  imply  that  some  have 
held  that  view,  and  declare  against  the  opinion  of 
those  some>   without  a  distinct  statement   that    he 
himself  had  been  one  of  them  :    still  less  does  he 
quietly  and  secretly  alter  what  he  had  previously 
published,    or   allowed   to    be  published,   so    as    to 
turn    the    old    view    into    the    new    one,    and    to 
leave   the  reader  to  understand  that  he  had  never 
changed  his  opinion.      The  Newton  of  the  mytho- 
logists  would  have    felt    to    his    fingers'  ends    that 
such   a   proceeding    had    a    tendency  to    give  false 
impressions  as  to  the  case,  and  to  throw  suspicion 
on  his  own  motives.      This  is  a  small  matter,  but  it 
is    a    commencement  of  worse.      We  come  to  the 
Commercium    Epistolicum,   the    name   given   to  the 
collection  of  letters,   accompanied  by  notes  and  a 
decision  of  the  question,    on    the  part  of  a  Com- 
mittee of  the  Royal  Society.      To  this  well-known 


154          REVIEW  OF  BREWSTERS 

part  of  the  history  Sir  D.  Brewster  has  a  very 
important  addition  to  make  ;  and  he  makes  it 
fairly,  though  we  confess  we  wish  he  had  given  us 
what  they  call  chapter  and  verse.  "It  is  due 
to  historical  truth  to  state  that  Newton  supplied 
all  the  materials  for  the  Commercium  Epistolicum, 
and  that  though  Keill  was  its  editor,  and  the  Com- 
mittee of  the  Royal  Society  the  authors  of  the 
Report,  Newton  was  virtually  responsible  for  its 
contents.1 

Before  we  proceed  further,  we  must  address  a 
respectful  word  to  Lord  Portsmouth,  the  descendant 
of  Newton's  niece,  the  representative  of  his  blood, 
and  the  possessor  of  these  valuable  papers,  to  whose 
liberality  and  judgment  the  permission  to  publish 
their  contents  is  due,  after  long  concealment  from 
fear  of  hurting  Newton's  reputation,  and  long 
abeyance  from  family  circumstances.  We  submit 
to  him  that  either  too  much  is  done,  or  not  enough. 
Great  harm  arose  out  of  the  rumours  which  circulated 
during  the  period  in  which  the  papers  were  con- 
cealed :  both  the  opponents  and  the  defenders  of 
Newton's  conduct  were,  without  any  fault  of  their 
own,  put  in  a  wrong  position  as  to  interpretation  of 
facts  and  appreciation  of  probabilities.  Much  more 

1  [See  Brewster,  Memoirs,  1855,  vol.  ii,  p.  75.  From  a  study  of  the 
"Portsmouth  Papers,"  Brewster  was  enabled  to  confirm  De  Morgan's 
contention  of  1852  that  Newton  wrote  the  anonymous  preface  to  the 
second  edition  of  the  Commercium  Epistolicum.  On  De  Morgan's 
rather  later  view  of  Newton's  character,  see  the  second  Appendix  to 
this  Essay.] 


"MEMOIRS    OF  NEWTON"          155 

harm  will  be  done  if  the  regretful  admissions  of  so 
warm  a  partisan  as  Sir  D.  Brewster  be  allowed  to 
stand  instead  of  these  rumours.  The  papers  cannot 
possibly  contain  anything  from  which  any  such 
injury  would  arise  as  unquestionably  will  arise  from 
the  above  substitution,  which,  to  all  the  indefinite- 
ness  of  mere  rumour,  adds  all  the  authority  of  a 
judicial  decision.  For  when  Sir  D.  Brewster  declares 
against  Newton,  it  is  as  if  a  counsel  threw  up  his 
brief:  we  mean  nothing  disrespectful,  for  we  re- 
member when  we  ourselves  would  have  held  it,  on 
such  retainers  as  the  Principia,  the  fluxions,  and 
the  optics.  Why  should  not  these  papers  be 
published  ?  It  must  come  to  this  at  last.  We 
have  little  doubt  that  the  Government  would  defray 
the  expense,  which  would  be  considerable  :  and  the 
Admiralty  publication  of  the  Flamsteed  papers 
would  be  a  precedent  of  a  peculiarly  appropriate 
character.  Those  who  were  scandalised  at  the  idea 
of  the  nation  paying  for  the  printing  of  an  attack 
upon  Newton  would  take  it  as  reparation  :  while 
those  who  entirely  approved  of  the  proceeding  would 
as  heartily  approve  of  the  new  measure.  It  is  im- 
possible that  the  matter  should  rest  here.  Sir 
D.  Brewster  himself  will  probably  desire,  for  his 
own  sake,  for  that  of  Newton,  and  for  that  of  truth, 
that  these  documents  should  undergo  public  scrutiny. 
And  we  have  no  delicacy  in  saying  that  they  ought 
to  come  under  the  eyes  of  persons  familiar  with  the 


156          REVIEW  OF  BREWS TER'S 

higher  parts  of  mathematics,  which  Sir  D.  Brewster 
neither  is,  nor  pretends  to  be.1 

The  Committee  of  the  Royal  Society  was  always 
considered  in  England  as  judicial,  not  as  expressly 
defensive  of  Newton.  A  few  years  ago,  Professor 
De  Morgan,  a  decided  opposer  of  Newton  and  the 
Committee  in  the  fluxional  dispute — and  one  whose 
views  Sir  D.  Brewster  states  himself  to  have  con- 
firmed on  several  points — rescued  the  objects  of  his 
censure  from  the  inferences  which  this  notion  would 
lead  to,  and  showed  that  the  Royal  Society  intended 
its  Committee  for  purposes  of  advocacy,  and  that 
the  members  of  the  Committee  had  no  other  idea 
of  their  own  function.  Sir  D.  Brewster  says  that 
Newton  himself  asserted  this  also  :  he  does  not  say 
where,  and  this  is  only  one  of  several  obiter  dicta 
which  ought  to  have  been  supported  by  reference  ; 
we  remember  no  such  statement.  It  is  now  of 
course  perfectly  settled  that  the  Committee  was  not 
judicial  ;  and  we  find  Newton  to  have  been  the  real 
source  of  the  materials  of  the  Commercium  Epistoli- 
cumy  and  answerable  for  all  the  running  notes  which 
accompany  the  published  correspondence.  We 
might  easily  proceed  to  justify  our  assertion  that 
his  moral  intellect  was  undergoing  deterioration  : 
but,  for  want  of  space,  we  shall  pass  on  to  1716, 
and  shall  make  one  extract  from  his  letter  to  Conti, 

1  [For  a  later  utterance  of  De  Morgan's  about  the  necessity  of 
publishing  the  "  Portsmouth  Papers,"  see  Newton  ;  his  Friend :  and  his 
Niece,  London,  1885,  pp.  148-149.] 


"MEMOIRS    OF  NEWTON"          157 

in  which,  in  his  own  name,  he  makes  the  assertion 
that  Leibniz  had  stolen  from  him.  He  says  that 
he  had  explained  his  ' '  method  "  to  Leibniz,  ' '  partly 
in  plain  words  and  partly  in  cyphers,"  and  that 
Leibniz  "disguised  it  by  a  new  notation  pretending 
that  it  was  his  own."  His  statement  contains  two 
untruths,  which  we  impute  to  the  forgetfulness  of 
irritation.  He  did  not  describe  part  of  his  method 
in  plain  words  :  all  that  he  described  in  plain  words 
was  the  species  of  problems  which  he  could  solve. 
When  Glendower  said,  "  I  can  call  spirits  from  the 
vasty  deep,"  no  one  ever  supposed  that  he  "partly 
described"  the  "method"  of  doing  it.  Secondly, 
he  did  not  describe  the  rest  in  cypher :  he  put  the 
letters  of  his  sentences  into  alphabetical  order,  and 
gave  what  was  called  an  anagram.  There  are  many 
good  decypherers  in  the  country,  and  the  task  is 
one  for  a  mathematician  :  Wallis  in  past  times,  and 
Mr  Babbage  now,  may  be  cited  as  instances.  But 
no  one  will  undertake  to  say  what  the  sentence  is 
which  we  have  decomposed  into  the  following  string 
of  letters  :  6a  2c  $d  196  2f  sh  $ij  $kl  6n  50  8r  93  9t 
3u  2vw  3y  ;  ninety-three  letters  in  all,  six  of  which 
are  a's,  two  are  c's,  etc. 

Yet  a  few  years  more,  and  the  deterioration  is 
more  decided.  In  1722,  Newton  himself  wrote  a 
preface  and  an  Ad  Lectorem  to  the  reprint  of  the 
Commercium  Epistolicum,  and  caused  to  be  prefixed 
a  Latin  version  of  the  account  of  that  work  which 


158          REVIEW  OF  BREWS  TER'S 

he  had  inserted  anonymously  in  the  Philosophical 
Transactions  for  1715.  His  authorship  of  this 
paper,  constantly  denied,  and  for  very  cogent 
reasons,  by  his  partisans,  but  proved  from  evidence 
internal  and  external,  is  now  admitted  by  Sir  D. 
Brewster.  Much  is  to  be  got  from  those  documents, 
but  we  shall  only  add  that  a  few  years  ago  Mr  De 
Morgan  discovered  that  some  alterations,  one  in 
particular  of  great  importance,  had  been  made  in 
this  reprint,  without  notice.  Of  .this  Sir  D.  Brewster 
says  not  one  word.  He  calls  the  reprint  a  new 
edition,  which  it  was  not  :  so  completely  doesut  pro- 
fess to  be  only  a  reprint,  that  the  old  title-page,  and 
the  old  date,  are  reprinted  after  the  new  title,  and 
the  avowedly  new  matter  at  the  beginning.  We 
now  believe  that  Newton  was  privy  to  the  altera- 
tions, and  especially  to  the  most  important  of  all : 
we  believe  it  independently  of  what  may  possibly 
arise  from  further  scrutiny  ;  and  we  suppose  from 
Sir  D.  Brewster's  silence  that  he  has  no  means  of 
contradicting  this  natural  inference.  The  famous 
letter  of  Newton  to  Collins,  on  which  the  Committee 
(very  absurdly)  made  the  whole  point  turn,  was 
asserted  to  have  been  sent  to  Leibniz,  but  no  date  of 
transmission  was  given  with  the  letter,  though  the 
report  of  the  Committee  affirmed  a  rough  date  of 
which  nothing  was  said  in  their  evidence.  A  date  of 
transmission  was  smuggled  into  the  reprint.  Where 
does  this  date  first  appear  ?  Who  first  gave  it  ? 


"MEMOIRS    OF  NEWTON"          159 

Newton  himself  in  the  Philosophical  Transactions, 
anonymously,  and  without  stating  any  authority. 

Lastly,  in  the  third  edition  of  the  Principia, 
Newton  struck  out  the  scholium  in  which  he  had 
recognised  the  rights  of  Leibniz.  It  has  been 
supposed  that  Pemberton,  who  assisted  him,  was 
the  real  agent  in  this  ' '  perhaps  unwise  "  step  :  but 
it  appears  distinctly  that  Newton  alone  is  responsible. 
He  struck  out  this  scholium  ;  did  he  state  openly 
why,  and  let  his  reader  know  what  had  been  done  ? 
He  supplied  it  by  another  scholium,  beginning  and 
ending  in  words  similar  to  the  old  one,  but  describ- 
ing, not  the  correspondence  with  Leibniz,  but  the 
celebrated  letter  to  Collins.  If  the  old  scholium 
had  been  misunderstood,  as  Newton  affirms  it  was, 
nothing  would  have  been  more  easy  than  to  annex 
an  explanation  :  if  the  suppression  were  done  openly. 
Newton,  in  the  second  edition  of  the  Principia,  had 
revenged  himself  on  Flamsteed  by  omitting  Flam- 
steed's  name  in  every  place  in  which  he  could 
possibly  do  without  it  :  the  omission  of  his  candid 
and  proper  acknowledgment  of  what  had  passed 
between  himself  and  Leibniz  was  but  a  repetition 
of  the  same  conduct  under  more  aggravated  circum- 
stances. Of  this  letter  to  Collins,  asserted  to  have 
been  sent  to  Leibniz,  and  falsely,  as  proved  in  our 
own  day  both  from  what  was  sent  to  Leibniz,  now 
in  the  Library  at  Hanover,  and  from  the  draught 
which  has  turned  up  in  the  archives  of  the  Royal 


160          REVIEW  OF  BREWS  TER'S 

Society,  we  shall  only  say  that  it  proved  that 
Newton  was  more  indebted  to  Hudde  than  Leibniz 
would  have  been  to  him  if  he  had  seen  the  letter. 
But  the  relations  of  Hudde  to  the  two  inventors 
of  the  differential  calculus  would  be  matter  for  a 
paper  apart. 

VII 

To  discuss  every  subject  would  require  volumes  ; 
and  we  shall  therefore  now  pass  on  to  Sir  D. 
Brewster's  treatment  of  the  curious  question  of  the 
relation  which  existed  between  Newton's  half  niece, 
Catherine  Barton,  and  his  friend  and  patron, 
Charles  Montague,  Earl  of  Halifax.  Sir  D.  Brew- 
ster  declares  that  for  a  century  and  a  half  no  stain 
has  been  cast  on  the  memory  of  Mrs  C.  Barton,  and 
then  proceeds  to  quote  Voltaire's  insinuation  as 
scarcely  deserving  notice;  so  that  by  "no  stain" 
we  are  to  understand  no  stain  which  he  thinks 
worthy  of  notice.  Now  the  fact  is  that,  though 
respect  for  Newton  has  kept  the  matter  quiet,  there 
has  always  been  a  general  impression  that  it  was  a 
doubtful  question,  a  thing  to  be  discussed,  whether 
or  no  Mrs  C.  Barton  was  the  mistress  of  Lord 
Halifax.  Mr  De  Morgan  took  up  this  subject  in 
the  Notes  and  Queries  (No.  210),  and,  perfectly 
satisfied  that  she  was  either  a  wife  or  a  mistress, 
came  to  a  balanced  conclusion  that,  as  he  says, 
*  *  the  supposition  of  a  private  marriage,  generally 


"MEMOIRS    OF  NEWTON"          161 

understood  among  the  friends  of  the  parties,  seems 
to  me  to  make  all  the  circumstances  take  an  air  of 
likelihood  which  no  other  hypothesis  will  give  them  : 
and  this  is  all  my  conclusion."  Sir  D.  Brewster, 
whose  mind  admits  no  such  balance,  makes  this 
the  * '  inference  "  of  a  private  marriage.  The  grounds 
of  the  alternative  are  that  she  was  publicly  declared, 
by  the  writer  of  the  Life  of  Halifax,  to  have  lived, 
when  very  young,  and  she  herself  distinguished  by 
beauty  and  wit,  in  the  house  of  Lord  Halifax  as 
"superintendent  of  his  domestic  affairs  ":  and  this 
not  in  attack,  but  defensively,  with  a  declaration 
that  she  was  a  virtuous  woman,  though  "  those  that 
were  given  to  censure  passed  a  judgment  upon  her 
which  she  no  ways  merited."  Further,  Lord  Halifax 
held  in  trust  an  annuity  for  her  of  £200  a  year, 
bought  in  Newton's  name  :  besides  which  he  left  her 
£5000,  with  Bushy  Park  and  a  manor  for  life  : 
while  neither  she  nor  any  one  of  her  friends  con- 
tradicted the  admission  made  in  the  Life  of  Halifax, 
which  came  out  at  the  time  when  the  legacies  and 
the  annuity  would  have  turned  public  attention 
upon  Miss  Barton.  This  is  a  subject  unconnected 
with  mathematics  ;  and  we  dwell  upon  it  more  than 
its  intrinsic  importance  deserves,  because  it  will 
enable  us  to  show  to  every  reader  the  kind  of 
reasoning  which  can  be  pressed  into  the  service  of 
biography,  when  biography  herself  has  been  tempted 

into   the    service  of  partisanship.      We    may  judge 

u 


162          REVIEW  OF  BREWSTERS 

from  the  arguments  which  Sir  David  is  driven  to 
employ,  that  he  would  have  followed  the  example 
of  other  biographers  in  slurring  this  subject,  if  Mr 
De  Morgan's  closing  words  had  not  reminded  him 
that  the  day  for  such  a  suppression  was  past  :  "  such 
points,  relating  to  such  men  as  Newton,  will  not 
remain  in  abeyance  for  ever,  let  biographers  be  as 
timid  as  they  will."  And  we  may  also  judge  from 
these  arguments  why  it  is  that  the  subject  has  been 
allowed  to  remain  in  abeyance. 

And   first,   as  to  the  annuity.      Halifax  holds  in 
trust  an  annuity  for  Miss  Barton,   and  directs    his 
executor    to    give  her  all  aid  in  the  transfer  :    this 
annuity    was    bought    in    Newton's    name.      Sir  D. 
Brewster  declares    that    "an  annuity  purchased  in 
Sir  Isaac  Newton's  name  can  mean  nothing  else  than 
an  annuity  purchased  by  Sir  Isaac  Newton."     This 
is  an  assertion  of  desperation — it  could  have  meant, 
not  thereby  saying  that  it  did  mean,  a  settlement 
by  Halifax  on  Miss  Barton,  done  in  Newton's  name, 
with  or  without  Newton's  knowledge  ;  and  done  in 
Newton's  name  purposely  that  people  might  think  it 
was  made  by  Newton,  or,  at  least,  not  by  Halifax. 
This  may  appear  impossible  to  Sir  D.  Brewster  in 
1855,  and  yet  it  may  have  been  done  in  1706.      We 
may  fairly  infer  that  Halifax  did  not  draw  his  will  with 
the  intention  of  giving  colour  to  those  reports  against 
which  his  biographer  protests,  or  with  the  intention  of 
exciting  such  reports  :  if  the  annuity  were  bought  by 


"MEMOIRS    OF  NEWTON"          163 

Newton,  what  more  easy  than  to  have  said  so?  In 
spite  of  Sir  D.  Brewster,  who  is  neither  lawyer  nor 
actuary,  we  affirm  positively  that  the  description  of 
an  annuity  upon  the  life  of  A  B  as  bought  in  the 
name  of  C  D,  does  not  imply  that  C  D  paid  for 
it,  and  that  so  far  as  it  implies  anything  on  the 
point,  which  is  little  enough,  it  is  the  very  contrary. 
Again,  Conduitt  does  not  mention  this  annuity  in 
his  list  of  the  benefactions  which  Newton,  who  was 
very  generous  to  his  family,  bestowed  on  his  poorer 
relations.  For  this  Sir  D.  Brewster  has  to  find  a 
reason  ;  Conduitt  was  the  husband  of  Catherine 
Barton,  knew  of  the  assertions  in  Halifax's  bio- 
graphy, had  read  Halifax's  will,  and  must  have  been 
cognisant  of  the  fact  that  the  existence  of  a  scandal 
had  been  asserted  in  print.  And  he  finds  a  curious 
reason. 

' '  But  the  annuity  was  not  a  benefaction  like 
those  contained  in  Conduitt's  list.  It  was  virtually 
a  debt  due  to  his  favourite  niece  whom  he  had 
educated,  and  who  had  for  twenty  years  kept  his 
house  ;  and  if  she  had  not  received  it  from  Sir  Isaac, 
his  conduct  would  have  been  very  unjust,  as,  owing 
to  his  not  having  made  a  will,  she  got  only  the 
eighth  part  of  his  personal  estate  along  with  his 
four  nephews  and  (three  other)  nieces." 

Let  us  first  take  Sir  D.  Brewster's  statement,  as 
here  given,  erroneous  as  it  is.  When  a  single  man 
educates  a  favourite  niece,  thereby  distinguishing  her 
from  his  other  nieces,  and  gives  her  shelter  and  main- 


1 64          REVIEW  OF  BREWSTER'S 

tenance  until  she  marries  (for  we  must  here  take  Sir 
D.  Brewster's  assertion  that  she  did  not  leave  him  to 
live  with  Lord  Halifax),  all  the  world  knows  that  the 
least  that  favourite  niece  can  do  is  to  keep  house  for 
him,  and  that  the  idea  of  her  services  in  looking  after 
the  dinner,  which  he  pays  for  and  gives  her  share  of, 
running  him  into  debt,  actual  or  virtual  (oh,  the 
virtue  of  this  word  !),  is  an  absurdity.  No  doubt  a 
man  ought  to  provide  for  such  a  niece  after  his 
death  :  but  if  he  should  leave  her,  as  Newton  did  to 
Miss  Barton,  the  eighth  part  of  ,£32,000,  producing 
an  income  of  more  than  £200  a  year,  he  treats  her 
very  handsomely  :  especially  if  a  friend  of  his  should 
have  left  her  a  large  fortune,  and  his  introduction 
should  have  married  her  to  a  member  of  Parliament. 
Now  to  Sir  D.  Brewster's  statement.  Just  before  our 
quotation  begins,  he  informs  us  that  by  the  act  of 
transference  it  appears  that  this  trust  was  created  in 
1706,  so  that  he  seems  to  say  that  Miss  Barton,  aged 
six  years,  began  to  keep  Newton's  rooms  in  Trinity 
College,  when  he  was  writing  the  Principia  :  for  he 
says  she  * '  had  "  kept  his  house  for  twenty  *  years. 
He  does  not  mean  this  :  but  here  and  elsewhere  he 

1  Conduitt  tells  us  that  his  wife  lived  with  her  uncle  nearly  twenty 
years,  before  and  after  her  marriage  :  it  is  believed  that  the  Conduitts 
resided  with  Newton  from  the  very  marriage.  Newton  lived  in  London 
thirty  years  ;  therefore,  ten  or  more  of  those  years  his  niece  did  not 
live  with  him.  The  annuity  was  bought  in  1706  and  Halifax  died  in 
1715.  Miss  Barton,  being  sixteen  years  old  when  Newton  came  to 
London,  must  have  finished  her  school  education  shortly  afterwards. 
Either  Newton  did  not  invite  his  favourite  niece,  whom  he  had  educated, 
to  live  with  him  for  ten  years  afterwards,  or  there  is  a  gap  which  tallies 
most  remarkably  with  the  hypothesis  of  her  residence  under  the  roof  of 


"MEMOIRS    OF  NEWTON"  165 

heaps  circumstances  together  without  sufficient  atten- 
tion to  consistency.  We  very  much  doubt  if  Newton 
could  have  afforded  the  price  of  that  annuity  in  1 706. 
He  came  to  London  with  very  little  in  1696  :  by 
1 706  he  had  enjoyed  £600  a  year  for  four  years,  and 
;£i  500  a  year  for  six  years.  An  annuity  of  £200  on 
a  life  of  twenty-six,  money  making  five  per  cent, 
now  costs  about  £3000 :  if  we  say,  which  is  straining 
the  point  to  the  utmost,  that  Miss  Barton's  annuity 
cost  £2000,  we  confess  we  think  it  not  very 
likely  that  Newton  could  have  bought  it,  or  that  he 
would  have  held  it  just  to  his  other  relatives  to  have 
bought  so  large  an  annuity.  But  we  are  quite  sure 
that  Conduitt,  under  all  the  circumstances,  would 
never  have  held  this  annuity  as  payment  of  a  debt 
due  to  his  wife  ;  he  would  not  have  made  the  twenty 
years  end  with  1706,  to  speak  of  nothing  else. 

Next,  we  come  to  the  way  in  which  Sir  D.  Brewster 
treats  the  assertions  of  Halifax's  biographer.  Those 
assertions  are  not  in  attack,  but  in  defence  ;  the 
witness  is  a  friendly  one,  and  the  publication  was 
made  at  the  very  time  when  Halifax's  will  had  just 
drawn  public  attention  to  the  legacies. 

Halifax.  But,  as  a  presumption  against  the  first  supposition,  there  is 
extant  a  short  letter  from  Newton  to  his  niece,  written  in  1700,  which 
by  the  contents  seems  written  to  an  inmate  of  his  house,  absent  for 
change  of  air. 

Newton  has  been  charged  with  avarice  ;  of  which  there  is  really  no 
proof,  unless  his  dying  worth  more  than  ^"30,000  be  one.  But  Conduitt 
was  in  easy  circumstances,  and  his  wife  also:  their  daughter  was  said 
to  have  had  ,£60,000.  Supposing,  as  is  probable,  that  they  bore  their 
fair  share  of  the  joint  expenses,  Newton  might  have  saved  nearly  all  his 
income  for  the  last  ten  years  of  his  life. 


1 66          REVIEW  OF  BREWS  TER'S 

"I  am  likewise  to  account  for  another  Omission 
in  the  Course  of  this  History,  which  is  that  of  the 
Death  of  the  Lord  Halifax's  Lady  ;  upon  whose 
Decease  his  Lordship  took  a  Resolution  of  living 
single  thence  forward,  and  cast  his  Eye  upon  the 
Widow  of  one  Colonel  Barton,  and  Neice  to  the 
famous  Sir  Isaac  Newton,  to  be  Superintendent  of 
his  domestic  Affairs.  But  as  this  Lady  was  young, 
beautiful  and  gay,  so  those  that  were  given  to  censure, 
pass'd  a  Judgment  upon  her  which  she  no  Ways 
merited,  since  she  was  a  Woman  of  strict  Honour  and 
Virtue  ;  and  tho'  she  might  be  agreeable  to  his  Lord- 
ship in  every  Particular,  that  noble  Peer's  Com- 
plaisance to  her,  proceeded  wholly  from  the  great 
Esteem  he  had  for  her  Wit  and  most  exquisite 
Understanding,  as  will  appear  from  what  relates  to 
her  in  his  Will  at  the  Close  of  these  Memoirs." 

Now  Sir  D.  Brewster  is  so  far  biased  by  the 
necessities  of  his  case,  as  to  affirm  that  it  is  not 
here  stated  that  Miss  Barton  (that  she  had  been 
married  is  a  mistake)  lived  under  Halifax's  roof. 
"  His  biographer  makes  no  such  statement.  .  .  . 
How  could  any  person  contradict  the  cast  of  an  eye 
— the  only  act  ascribed  to  Halifax  by  his  bio- 
grapher ?  "  The  writer  of  * '  Newton  "  in  the  Bio- 
graphia  Britannica — as  strong  a  partisan  as  Sir 
David — could  not  get  so  far  as  this  ingenious 
solution :  for  he  makes  Halifax's  continuance  in 
his  widowed  state  "the  less  to  be  regretted"  on 
account  of  this  ' '  cast  of  an  eye. "  We  are  to  infer, 
according  to  Sir  David,  that  this  friendly  biographer, 
wishing  to  defend  Miss  Barton  from  censure  she  no 


"MEMOIRS    OF  NEWTON"  167 

ways  deserved,  and  alluding  to  rumours  which  had 
no    source    except    a    "plan    or   a    wish"  of  Lord 
Halifax,   omitted   to    state    that    the    plan    was  all 
Montague's    eye ;    and    forgot    to   assert    the   very 
material  circumstance  that  she  did  not  accede  to  the 
plan,  that  she  did  not  live  in  the  house  of  her  earnest 
admirer.      We  make  no  doubt,  on  the  other  hand, 
that  the  apologist  means  to  say  that  she  did  live 
there,  and  made  her  a  widow  to  give  some  colour 
of  respectability  to  it.      Her  noble  admirer  left  his 
large    legacy    "as    a    token,"    he    writes,    "of   the 
sincere  love,  affection,  and  esteem,  I  have  long  had 
for  her  person,  and  as  a  small  recompence  for  the 
pleasure  and  happiness  I  have  had  in  her  conversa- 
tion."     Sir  D.    Brewster  appends  a  note    to   prove 
that  love  and  affection  "had  not,  in  Halifax's  day, 
the    same   meaning   which  they  have  now."     Does 
he  really  think  that  they  mean  nothing  now  except 
conjugal  love  and  its  imitations  ?     Does  not  a  man 
still  love  his  friends,   and  might  not  Pope  write  to 
H.    Cromwell    now,   as    then,   of   his   affection    and 
esteem  ?     If   we   come  to  old  meanings,   we  might 
remember    that    conversation  did  not  always  mean 
colloquy.^-     If    Miss    Barton    did   live   with   Halifax 
under  one  roof,  and  if  Halifax  did  buy  the  annuity, 
these  words  are  to  be  interpreted  accordingly.      And 
they  must  be  looked  at  jointly  with  the  other  things. 

1  [On  the  old  meaning  of  the  word  "conversation,"  see  De  Morgan, 
Newton:  his  Friend:  and  his  Niece,  London,  1885,  pp.  58-64.] 


1 68          REVIEW  OF  BREWSTER'S 

There  Is  a  fallacy  which  has  no  name  in  books  of 
logic,  but  is  of  most  frequent  occurrence.  It  is  that 
because  neither  A,  nor  B,  nor  C,  will  separately 
give  moral  conviction  of  D,  that  therefore  they  do 
not  give  it  when  taken  together. 

We  have  seen  that  Sir  D.  Brewster  can  omit,  as 
in  the  case  of  the  secret  alterations  in  the  reprint 
above  mentioned :  we  shall  now  see  that  he  can 
omit  when  he  distinctly  declares  he  has  not  omitted. 
We  are  far  from  charging  him  with  any  unfair  in- 
tention :  we  know  the  effect  of  bias,  and  nothing 
disgusts  us  more  than  the  readiness  with  which 
suppressions  and  misrepresentations  are  set  down 
to  deliberate  intention  of  foul  play.  Sir  D.  Brewster 
informs  us  that  he  has  given  in  an  appendix  ' '  all 
the  passages  "  in  which  Swift  mentions  Miss  Barton 
or  Halifax.  He  has  not  given  all.  When  he  wrote 
this  (vol.  ii,  p.  278),  he  intended  to  give  all ;  but 
when  he  came  to  the  appendix,  he  altered  his  mind, 
omitted  two,  and  forgot  his  previous  announcement. 
It  was  not  oversight,  because  Mr  De  Morgan  had 
particularly  mentioned  these  curious  passages,  in 
which  Swift  quotes  to  Stella  some  of  Miss  Barton's 
conversation,  which  has  the  freedom  of  a  married 
woman  (we  mean  of  that  day ;  our  matrons  are 
more  particular).  Either  the  Professor,  who  de- 
clines to  repeat  the  stories,  is  overfastidious,  or  is 
unskilful  in  rendering  the  license  of  the  seventeenth 
century  into  the  decorums  of  the  nineteenth  :  we 


"MEMOIRS    OF  NEWTON*  169 

think  we  can  convey  an  idea  of  the  good  joke  over 
which  Catherine  Barton,  aged  31,  and  Jonathan 
Swift,  aged  43,  enjoyed  a  hearty  laugh.  A  man 
had  died,  leaving  small  legacies  to  those  who  should 
bear  him  to  the  grave,  who  were  to  be  an  equal 
number  of  males  and  females  :  provided  always  that 
each  bearer,  male  or  female,  should  take  a  declara- 
tion that  he  or  she  had  always  been  a  strict  votary 
of  Diana.  The  joke  was,  that  there  lay  the  poor 
man,  unburied,  and  likely  to  remain  so  :  and  this 
was  the  joke  which  Miss  Barton  introduced,  in  a 
tete-a-tete  with  Swift ;  at  least  so  says  Swift  him- 
self. Mr  De  Morgan  thinks  that  ' c  Swift's  tone 
with  respect  to  the  stories,  combined  with  his 
obvious  respect  for  Mrs  Barton,  may  make  any  one 
lean  to  the  supposition  that  he  believed  himself  to 
be  talking  to  a  married  woman."  Certainly  it  can 
hardly  be  credited  that  the  maiden  niece  of  Newton 
(then  living  in  Newton's  house,  according  to  Sir  D. 
Brewster)  would  bring  up  such  a  joke  for  the  enter- 
tainment of  a  bachelor  friend  :  and  Swift's  great  and 
obvious  respect  for  Catherine  Barton  will  justify  us 
in  thinking  that  he  never  would  have  invented  such 
a  story  as  coming  from  her. 

We  do  not  intend  to  decide  the  question  whether 
the  lady  was  the  platonic  friend,  the  mistress,  or  the 
secretly  married  wife,  of  Lord  Halifax  :  in  conse- 
quence of  the  reserve  of  biographers,  it  has  never 
been  fully  put  forward  until  our  own  day.  Further 


1 70          REVIEW  OF  BREWS  TER'S 

research  may  settle  it  :  what  we  have  to  do  with  is 
our  biographer's  mode  of  dealing  with  his  case.      Sir 
D.    Brewster    certainly  handles    the    phenomena  of 
mind    and   conduct  as  if   they  were  phenomena  of 
matter  :  he  requires  that  any  conclusion  shall  be  a 
theory,  which  is  to  explain  how  all  the  circumstances 
arose.      No  such  thing  is  possible  in  grappling  with 
circumstantial  evidence  as  to  the  dealings  of  human 
beings    with    one    another.      Never    a    day    passes 
without  the  prisoner's  counsel  triumphantly  bringing 
to  notice  a  circumstance  which  is  perfectly  inexpli- 
cable on    the  supposition  of  his  client's  guilt.      So 
says  the  judge  too,  and  so  feel  the  jury  :  and  both 
parties  are  in  a    difficulty.      If   it  were  a   question 
about  an  explanatory  theory,  as  of  light,  an  obstinate 
dark  band  or  coloured  fringe  might  put  the  undula- 
tions out  of  the  question,  till  further  showing.      But 
the  court  asks  the  jury,  not  for  their  theory,  but  for 
their  verdict  :  that  verdict  is  guilty,  and  the  prisoner 
generally  confirms  it,  at  least  in  capital  cases,  and 
explains  the  difficulty.      The  matter  we  have  been 
discussing    has    two   counts :    the    first    opens    the 
question  whether,  under  the  circumstances,  the  con- 
clusion that  Miss  Barton  lived  with  Halifax  can  be 
avoided ;    the    second,    on    the    supposition    that    it 
cannot  be  avoided,  opens  the  question  whether  she 
lived  with  him  as  a  mistress  or  as  a  secretly  married 
wife.      Sir    D.    Brewster    works    hard    against    the 
supposition  of   the  marriage,   and,   by  an  ignoratio 


"MEMOIRS    OF  NEWTON"          171 

elenchi,  believes  himself  to  be  forwarding  his  own 
alternative  ;  but  we  strongly  suspect  that  his  reasons 
against  the  marriage,  be  their  force  what  it  may, 
will  not  avail  against  the  other  alternatives  of  our 
second  count.1 

VIII 

We  will  now  take  the  vexed  question  of  Newton's 
religious  opinions,  a  vexed  question  no  more,  for 
the  papers  so  long,  and,  in  the  first  instance,  so  un- 
worthily suppressed,  are  now  before  the  world.  Sir 
D.  Brewster,  in  his  former  Life,  followed  his  pre- 
decessors in  stoutly  maintaining  orthodoxy,  by  which, 

1  [De  Morgan  made  many  further  investigations  on  this  subject.  An 
article  on  Catherine  Barton  and  Halifax  was  written  by  him  in  1858  for 
The  Companion  to  the  Almanac,  This  article  was  rejected  by  Charles 
Knight,  the  editor,  who  thought  that  the  question  discussed  in  it  would 
not  be  held  generally  interesting  (see  also  Mrs  De  Morgan's  Memoir, 
1882,  p.  264).  The  original  manuscript  was  revised,  and  received  some 
additions  in  the  years  1864-6.  And,  later  still,  on  the  accession  of  new 
evidence,  it  was  enlarged  again.  It  was  published  posthumously,  under 
the  editorship  of  his  widow  and  his  pupil  A.  C.  Ranyard,  under  the 
title  Newton:  his  Friend:  andliis  Niece  (London,  1885).  This  book 
contains  many  digressions,  most  of  which  are  interesting  and  some  of 
which  are  amusing  ;  and  De  Morgan  concluded  that  a  private  marriage 
between  Halifax  and  Catherine  Barton  was  contracted  in  1706.  The 
most  important  piece  of  evidence  is  a  letter  in  Newton's  handwriting, 
dated  in  May  1715,  bought  by  De  Morgan's  friend  Guglielmo  Libri — 
who  was  accused  and  proceeded  against  by  the  French  government, 
unjustly  it  seems,  of  having  stolen  books  from  public  libraries  in  France 
— in  1856,  which  contains  the  sentence  :  "  The  concern  I  am  in  for  the 
loss  of  my  Lord  Halifax,  and  the  circumstances  in  which  I  stand  related 
to  his  family,  will  not  suffer  me  to  go  abroad  till  his  funeral  is  over." 
See  also  Mrs  De  Morgan's  Memoir,  p.  288.  Macaulay's  view  of  the 
question  was  (Newton  :  his  Friend:  and  his  Niece,  p.  70)  that  Catherine 
Barton  was  neither  Halifax's  mistress  nor  his  wife,  and  that  the  relation 
between  them  was  of  the  same  sort  as  that  between  Congreve  and  Mrs 
Bracegirdle,  as  that  between  Swift  and  Stella,  as  that  between  Pope 
and  Martha  Blount,  and  as  that  between  Cowper  and  Mrs  Unwin.  For 
De  Morgan's  view  of  Brewster's  treatment  of  the  Halifax  case,  see  ibid. , 
pp.  107-130  ;  the  case  is  discussed  in  Brewster's  Memoirs,  1855,  vol.  ii, 
pp.  270-281.] 


REVIEW  OF  BREWS TER'S 

in  this  article,  we  mean  a  belief  of  at  least  as  much 
as  the  churches  of  England  and  Scotland  hold  in 
*  common.  But  many  circumstances  seemed  to  point 
the  other  way.  There  was  a  strong  and  universal 
impression  that  Horsley  had  recommended  the  con- 
cealment of  some  of  the  "Portsmouth  Papers,"  as 
heterodox  :  and  here  and  there  was  to  be  found,  in 
every  generation,  a  person  who  had  been  allowed  to 
see  them,  and  who  called  them  dubious,  at  least. 
Newton  was  the  friend  of  the  heretics  Locke  and 
Clarke,  and  sent  abroad,  for  publication,  writings 
on  the  critical  correction  of  texts  on  which  Trini- 
tarians relied,  without  a  word  against  the  conclusion 
which  might  be  drawn  respecting  himself.  Nay,  he 
spoke  of  the  Trinity  in  a  manner  which  Sir  D. 
Brewster  admits  would  make  any  one  suspect  his 
orthodoxy.  Whiston,  always  indiscreet,  but  always 
honest,  declared  from  his  own  conversation  with 
Newton,  that  Newton  was  an  Arian  ;  Haynes, 
Newton's  subordinate  at  the  Mint,  declared  to  Baron, 
a  Unitarian  minister,  that  Newton  was  what  we  now 
call  a  Unitarian.  He  himself,  in  the  Principia, 
allowed  himself  a  definition  of  the  word  * '  God " 
which  would  have  permitted  him  to  maintain  the 
Deity  of  the  second  and  third  persons  of  the  Trinity. 
He  said  that  every  spiritual  being  having  dominion 
is  God  :  Dominatio  entis  spiritualis  Deuni  constituit. 
And  he  enforces  his  definition  by  so  many  exempli- 
fications that  it  is  beyond  question  he  means  that, 


"MEMOIRS    OF  NEWTON*          173 

if  the  Almighty  were  to  grant  some  power,  for  only 
five  minutes,  to  a  disembodied  spirit,  that  spirit 
would  be,  for  that  time,  a  God. 

In  the  papers  now  produced  for  the  first  time, 
we  have  certain  paradoxical  questions  (the  word 
"paradox"  then  meant  an  unusual  opinion)  con- 
cerning Athanasius  and  his  followers,  in  which  many 
historical  opinions  of  a  suspicious  character  are 
maintained  ;  but  no  matters  of  doctrine  are  touched 
upon.  In  ((  A  Short  Scheme  of  the  True  Religion," 
the  purpose  is  rather  to  describe  religion  as  opposed 
to  irreligion,  and  all  who  are  conversant  with  opinion 
know  that  a  Trinitarian  and  a  Unitarian  use  the 
same  phrases  against  atheism  and  idolatry.  Hence, 
some  language  which  in  controversy  would  be 
heterodox,  may  be  counted  orthodox.  But  in 
another  manuscript,  "On  our  Religion  to  God,  to 
Christ,  and  the  Church,"  there  is  an  articulate 
account  of  Newton's  creed,  in  formal  and  dogmatical 
terms.  This  we  shall  give  entire  :  and  it  is  to  be 
remembered  that  Newton  destroyed  many  papers 
before  his  death,  which  adds  to  those  he  left  behind 
him  additional  meaning  and  force. 

"Art.  i.  There  is  one  God  the  Father,  ever 
living,  omnipresent,  omniscient,  almighty,  the  maker 
of  heaven  and  earth,  and  one  Mediator  between  God 
and  man,  the  man  Christ  Jesus. 

*  *  Art.  2.  The  Father  is  the  invisible  God  whom 
no  eye  hath  seen,  nor  can  see.  All  other  beings 
are  sometimes  visible. 


174          REVIEW  OF  BREWS  TER'S 


1 1 


Art.  3.  The  Father  hath  life  in  himself,  and 
hath  given  the  Son  to  have  life  in  himself. 

' '  Art.  4.  The  Father  is  omniscient,  and  hath  all 
knowledge  originally  in  his  own  breast,  and  com- 
municates knowledge  of  future  things  to  Jesus 
Christ  ;  and  none  in  heaven  or  earth,  or  under  the 
earth,  is  worthy  to  receive  knowledge  of  future  things 
immediately  from  the  Father,  but  the  Lamb.  And, 
therefore,  the  testimony  of  Jesus  is  the  spirit  of 
prophecy,  and  Jesus  is  the  Word  or  Prophet  of 
God. 

"Art.  5.  The  Father  is  immovable,  no  place 
being  capable  of  becoming  emptier  or  fuller  of  him 
than  it  is  by  the  eternal  necessity  of  nature.  All 
other  beings  are  movable  from  place  to  place. 

"Art.  6.  All  the  worship  (whether  of  prayer, 
praise,  or  thanksgiving),  which  was  due  to  the 
Father  before  the  coming  of  Christ,  is  still  due  to 
him.  Christ  came  not  to  diminish  the  worship  of  his 
Father. 

'  *  Art.  7.  Prayers  are  most  prevalent  when 
directed  to  the  Father  in  the  name  of  the  Son. 

' '  Art.  8.  We  are  to  return  thanks  to  the  Father 
alone  for  creating  us,  and  giving  us  food  and  raiment 
and  other  blessings  of  this  life,  and  whatsoever  we 
are  to  thank  him  for,  or  desire  that  he  would  do  for 
us,  we  ask  of  him  immediately  in  the  name  of 
Christ. 

' '  Art.  9.  We  need  not  pray  to  Christ  to  intercede 
for  us.  If  we  pray  the  Father  aright  he  will 
intercede. 

"Art.  10.  It  is  not  necessary  to  salvation  to 
direct  our  prayers  to  any  other  than  the  Father  in 
the  name  of  the  Son. 

"Art.  ii.  To  give  the  name  of  God  to  angels  or 
kings,  is  not  against  the  First  Commandment.  To 
give  the  worship  of  the  God  of  the  Jews  to  angels 


"MEMOIRS    OF  NEWTON"  175 

or  kings  is  against  it.  The  meaning  of  the  com- 
mandment is,  Thou  shalt  worship  no  other  God 
but  me. 

' '  Art.  12.  To  us  there  is  but  one  God,  the  Father, 
of  whom  are  all  things,  and  one  Lord  Jesus  Christ, 
by  whom  are  all  things,  and  we  by  him.  That  is, 
we  are  to  worship  the  Father  alone  as  God  Almighty, 
and  Jesus  alone  as  the  Lord,  the  Messiah,  the  Great 
King,  the  Lamb  of  God  who  was  slain,  and  hath 
redeemed  us  with  his  blood,  and  made  us  kings  and 
priests. " 


In  a  paper  called  "  Irenicum,"  or  "  Ecclesiastical 
Polity  tending  to  Peace,"  are  many  remarks  on 
church-government,  but  on  doctrine  only  as  follows. 
After  insisting,  in  one  place,  that  those  who  intro- 
duce any  article  of  communion  not  imposed  from 
the  beginning  are  teaching  another  gospel,  he  gives, 
in  another  place,  the  fundamentals,  by  which  he 
means  the  terms  of  communion  imposed  from  the 
beginning. 

'  *  The  fundamentals  or  first  principles  of  religion 
are  the  articles  of  communion  taught  from  the  be- 
ginning of  the  Gospel  in  catechising  men  in  order  to 
baptism  and  admission  into  communion  ;  namely, 
that  the  catechumen  is  to  repent  and  forsake  covet- 
ousness,  ambition,  and  all  inordinate  desires  of  the 
things  of  this  world,  the  flesh,  and  false  gods  called 
the  devil,  and  to  be  baptized  in  the  name  of  one 
God,  the  Father,  Almighty,  Maker  of  Heaven  and 
Earth,  and  of  one  Lord  Jesus  Christ,  the  Son  of 


1 76          REVIEW  OF  BREWS  TER'S 

God,  and  of  the  Holy  Ghost.      See  Heb.  v.   12,  13, 
14,  and  vi.  i,  2,  3." 

In  some  queries  on  the  word  O/ULOOVO-LOS,  Newton 
asks,  among  many  questions  of  a  similar  tendency, 
whether  unius  substanticz  ought  not  to  be  consubstan- 
tialis — whether  hypostasis  did  not  signify  substance 
— whether  Athanasius,  etc.,  did  not  acknowledge 
three  substances — whether  the  worship  of  the  Holy 
Ghost  was  not  ' '  set  on  foot "  after  the  Council  of 
Sardica — whether  Athanasius,  etc. ,  were  not  Papists. 
We  prefer  giving  the  reader  Newton's  opinions  in  full 
to  arguing  on  them  ourselves.  It  would  be  difficult, 
we  think,  to  bring  him  so  near  to  orthodoxy  as 
Arianism.  Though  his  exposition  of  his  own 
opinions  goes  far  beyond  the  simple  terms  of  com- 
munion, there  is  not  a  direct  word  on  the  divinity 
of  Christ,  on  his  pre-existence,  on  the  miraculous 
conception,  on  the  resurrection,  on  the  personality 
of  the  Holy  Ghost,  or  on  the  authority  of  Scripture. 
Those  who  think  that  some  of  these  points  (as  we 
think  of  the  fourth  and  sixth)  must  be  implied,  will 
perhaps  bring  in  the  rest  :  but  those  who  look  at  the 
emphatic  first  article  of  the  twelve,  unmodified  and 
unqualified  by  the  rest,  though  enforced  by  the 
eighth  and  ninth,  will,  we  think,  give  up  the  point, 
and  will  class  Newton,  as  Haynes  did,  with  the 
Humanitarians,  and  not,  as  Whiston  did,  with  the 
Arians.  Sir  D.  Brewster  leaves  it  to  be  implied 
that  he  does  not  any  longer  dispute  the  heterodoxy 


"MEMOIRS    OF  NEWTON"  177 

of  Newton's  creed  ;  that  is,  its  departure  from  the 
creed  most  commonly  believed  by  Christians.  Of 
this  we  have  no  doubt,  that  in  his  theological 
opinions,  Newton  was  as  uncompromising  and  as 
honest  as  in  his  philosophical  ones.  And  he  was 
no  dabbler  in  the  subject,  having  in  truth  much 
reading,  both  as  a  scholar  and  a  theologian.1 

IX 

We  cannot  easily  credit  the  story  of  Newton  in 
love  at  sixty  years  of  age.  In  Conduitt's  hand- 
writing is  a  letter  entitled  "Copy  of  a  letter  to 
Lady  Norris  by  .  .  .  ,"  docketed,  in  another  hand, 
"A  letter  from  Sir  I.  N.  to  .  .  .  ."  The  letter  is 
amusing.  After  informing  the  lady  that  her  grief 
for  her  late  husband  is  a  proof  she  has  no  objection 
to  live  with  a  husband,  he  advises  her,  among  other 
things,  that  a  widow's  dress  is  not  acceptable  in 
company,  and  that  it  will  always  remind  her  of  her 
loss  :  and  that  '  *  the  proper  remedy  for  all  these 
mischiefs  is  a  new  husband "  ;  the  question  being 
whether  she  '  *  should  go  constantly  in  the  melancholy 
dress  of  a  widow,  or  flourish  once  more  among  the 
ladies."  Sir  D.  Brewster  seems  rather  staggered 
by  this  letter :  but  there  is  no  authority  for  it 
coming  from  Newton,  and  surely  we  may  rather 

1  [On  Newton's  religious  opinions,  see,  besides  §  XI.  of  the  first 
Essay,  above,  De  Morgan,  Newton:  his  Friend:  and  his  Niece,  London, 
1885,  p.  107.] 

12 


1 78          REVIEW  OF  BREWS  TER'S 

suspect  that  his  friend,  Lady  Norris,  sent  him,  or 
perhaps  Miss  Barton,  a  copy  of  a  letter  from  some 
coxcomb  of  a  suitor.1  Newton  was  always  a  man 
of  feeling,  right  or  wrong,  and,  though  perhaps  he 
would  have  been  awkward  at  the  expression  of  it, 
he  never  would  have  addressed  a  woman  for  whom 
he  experienced  a  revival  of  what  he  once  felt  for 
Miss  Storey,  in  such  terms  as  the  young  bucks  in 
the  Spectator  address  rich  widows.  The  letter 
reminds  us  much  more  of  Addison's  play,  and  of  the 
puppy  who  was  drummed  away  from  the  widow  by 
the  ghost,  than  of  Newton. 

X 

To  us  it  has  always  been  matter  of  regret  that 
Newton  accepted  office  under  the  Crown.  Sir  D. 
Brewster  thinks  otherwise.  "  At  the  age  of  fifty, 
the  high-priest  of  science  found  himself  the  inmate 
of  a  college,  and,  but  for  the  generous  patronage  of 
a  friend,  he  would  have  died  within  its  walls. "  And 
where  should  a  high-priest  of  science  have  lived  and 
died  ?  At  the  Mint  ?  Very  few  sacrifices  were 
made  to  science  after  Newton  came  to  London. 
One  year  of  his  Cambridge  life  was  worth  more  to 
his  philosophical  reputation  and  utility  than  all  his 
long  official  career.  If,  after  having  piloted  the 

1  The  original  letter,  written  shortly  after  1702,  is  copied  in  the 
handwriting  of  Conduitt,  who  did  not  become  a  member  of  Newton's 
family  till  1717.  Say  that  Lady  Norris  sent  it  to  Mrs  Conduitt,  to 
amuse  her,  and  that  Conduitt  copied  it. 


"MEMOIRS    OF  NEWTON"  179 

country  safely  through  the  very  difficult,  and  as 
some  thought,  impossible,  operation  on  the  coinage, 
he  had  returned  to  the  University  with  a  handsome 
pension,  and  his  mind  free  to  make  up  again  to  the 
"litigious  lady,"  he  would,  to  use  his  own  words, 
have  taken  "another  pull  at  the  moon,"  and  we 
suspect  Clairaut  would  have  had  to  begin  at  the 
point  from  which  Laplace  afterwards  began.  Newton 
was  removed,  the  high-priest  of  science  was  trans- 
lated to  the  temple  of  Mammon,  at  the  time  when 
the  differential  calculus  was,  in  the  hands  of  Leibniz 
and  the  Bernoullis,  beginning  to  rise  into  higher 
stories.  Had  Newton  remained  at  hi%s  post,  coining 
nothing  but  ideas,  the  mathematical  science  might 
have  gained  a  century  of  advance. 


XI 

We  now  approach  the  end  of  our  task,  and,  in 
in  spite  of  our  battle  with  the  biographer,  we  cannot 
express  the  pleasure  with  which  we  have  read  his 
work.  It  is  very  much  superior,  new  information 
apart,  to  the  smaller  Life  which  he  published  long 
ago.  Homer's  heroes  are  very  dry  automatons  so  long 
as  they  are  only  godlike  men  :  but  when  they  get 
into  a  quarrel  with  one  another,  out  come  the  points 
on  which  we  like  and  dislike.  Newton  always  right, 
and  all  who  would  say  otherwise  excathedrally  re- 
proved is  a  case  for  ostracism  ;  we  are  tired  of  hear- 


1 8o          REVIEW  OF  BREWSTERS 

ing  Aristides  always  called  the  just.  But  Newton 
of  whom  wrong  may  be  admitted,  Newton  who  must 
be  defended  like  other  men,  and  who  cannot  always 
be  defended,  is  a  man  in  whom  to  feel  interest  even 
when  we  are  obliged  to  dissent  from  his  eulogist. 
As  we  have  said  before,  it  is  the  defence  which  pro- 
vokes the  attack.  Newton,  with  the  weak  points 
exposed  and  unprotected,  is  not  and  cannot  be  an 
object  of  assault  :  our  blow  is  on  the  shield  which 
the  biographers  attempt  to  hold  before  him.  A 
great  predecessor  was  guilty  of  delinquencies  before 
which  the  worst  error  of  Newton  is  virtue  itself :  he 
sold  justice  for  bribes,  so  committing  wilful  perjury 
— for  who  may  dare  to  deny  that  the  oath  of  the 
false  judge  rose  before  his  mind  when  he  fingered 
the  price  of  his  conscience — that  the  perjury  itself 
is  forgotten  in  the  enormity  of  the  mode  of  commit- 
ting it.  But  how  often  is  this  remembered  when 
we  think  of  Bacon  ?  The  bruised  reed  is  not  broken, 
because  even  biographers  admit  that  it  is  a  bruised 
reed  :  let  them  hold  it  up  for  a  sturdy  oak,  and  the 
plain  truth  shall  be  spoken  whenever  the  name  is 
mentioned.  And  so,  in  its  degree,  must  it  be  with 
the  author  of  the  Principia. 

All  Newton's  faults  were  those  of  a  temperament 
which  observers  of  the  human  mind  know  to  be  in- 
capable of  alteration,  though  strong  self-control  may 
suppress  its  effects.  The  jealous,  the  suspicious 
nature,  is  a  part  of  the  man's  essence,  when  it  exists 


"MEMOIRS    OF  NEWTON"          181 

at  all  :  it  is  no  local  sore,  but  a  plague  in  the  blood. 
Think  of  this  morbid  feeling  as  the  constant  attend- 
ant of  the  whole  life,  and  then  say,  putting  all 
Newton's  known  exhibitions  of  it  at  their  very 
worst,  how  much  they  will  amount  to,  as  scattered 
through  twenty  years  of  controversy  with  his  equals, 
and  thirty  years  of  kingly  power  over  those  who 
delighted  to  call  themselves  his  inferiors.  Newton's 
period  of  living  fame  is  longer  than  that  of  Welling- 
ton :  it  is  easy  to  talk  of  sixty  years,  but  think  of 
the  time  between  1795  and  1855,  and  we  form  a 
better  image  of  the  duration.  In  all  this  life,  we 
know  of  some  cases  in  which  the  worst  nature  con- 
quered the  better  :  in  how  many  cases  did  victory, 
that  victory  which  itself  conceals  the  battle,  declare 
for  the  right  side  ?  Scott  claims  this  allowance  even 
for  Napoleon  ;  how  much  more  may  it  be  asked  for 
Newton  ?  But  it  can  only  be  asked  by  a  biographer 
who  has  done  for  the  opponents  of  his  hero  what  he 
desires  that  his  readers  should  do  for  the  hero  him- 
self. When  once  the  necessary  admissions  are  made, 
so  soon  as  it  can  be  done  on  a  basis  which  compro- 
mises no  truth,  and  affords  no  example,  we  look 
on  the  errors  of  great  men  as  straws  preserved  in 
the  pure  amber  of  their  services  to  mankind.  If  we 
could  but  know  the  real  history  of  a  flaw  in  a 
diamond,  we  might  be  made  aware  that  it  was  a 
necessary  result  of  the  combination  of  circumstances 
which  determined  that  the  product  should  be  a 


1 82  "MEMOIRS    OF  NEWTON" 

diamond,  and  not  a  bit  of  rotten  wood.  Let  a  flaw 
be  a  flaw,  because  it  is  a  flaw  :  Newton  is  not  the 
less  Newton ;  and  without  the  smallest  rebellion 
against  Locke's  maxim  —  whatever  it  is  —  nobis 
gratulamur  tale  tantumque  extitisse  humani  generis 
decus. 


APPENDIX  I.   TO  THE  THIRD  ESSAY 
(See  note  i  on  p.  148.) 

DE  MORGAN'S  VIEW  OF  LEIBNIZ'S  CHARACTER1 

THE  Leibniz  of  our  day  is  either  the  mathematician  or  the 
metaphysician. 

In  the  first  of  these  two  characters  he  is  coupled  in  the 
mind  of  the  reader  with  Newton,  as  the  co-inventor  of  what 
was  called  by  himself  the  Differential  Calculus,  and  by 
Newton  the  Method  of  Fluxions.  Much  might  be  instanced 
which  was  done  by  him  for  the  pure  sciences  in  other 
respects ;  but  this  one  service,  from  its  magnitude  as  a 

1  [The  following  is  from  a  biographical  sketch  entitled  "Leibnitz" 
which  appeared  anonymously  in  the  Gallery  of  Portraits :  with  Memoirs 
(vol.  vi,   1836,  pp.  132-136)  which  was  published  by  Charles  Knight 
at  London  under  the  superintendence  of  the  Society  for  the  Diffusion 
of  Useful  Knowledge.     We   know  from   Mrs  De  Morgan's   Memoir 
(p.  108),  that  this  article  was  by  De  Morgan.     "The  Life  of  Maske- 
lyne,"  she  says,  "  is  one  of  a  series  of  lives  of  Astronomers  written  by  him 
for  the  Gallery  of  Portraits •,  published  by  C.  Knight  two  or  three  years 
before  this  time  (1839).   They  are  those  of  Bradley,  Delambre,  Descartes, 
Dollond,  Euler,  Halley,  Harrison,  W.   Herschel,  Lagrange,  Laplace, 
Leibnitz,  and  Maskelyne.     They  are  bound  up  together,  and  illustrated 
in  his  own  way,  under  the  title  of  '  Mathematical  Biography,  extracted 
from  the  Gallery  of  Portraits,  by  Augustus  De   Morgan,  H.O.M.O. 
P.A.U.C.A.R.U.M.  L.I.T.E.R.A.R.U.M.'    The  letters  of  his  literary 
tail  were  only  B.A.,  F.R.A.S.,  besides  those  expressing  membership 
of  one  or  two  lesser  scientific  societies.     On  account  of  the  declaration 
of  belief  at  that  time  required  by  the  University,  he  never  took  his  M.  A. 
degree."     On  the  reference  to  Halley,  cf.  note  2  on  p.  21.     The  extract 
printed  above  is   on  pp.   134-136  of  the    Gallery.      The   portrait  of 
Leibniz   given   in   this  article  is  an  engraving  after  the  well-known 
picture  in  the  Florence  Gallery,  which  is  reproduced  in  the  Open  Court 
Company's  series  of  portraits  of  philosophers.  ] 

183 


1 84  CHARACTER 

discovery,  and   its   notoriety  as  the  cause  of  a  great  con- 
troversy, has  swallowed  up  all  the  rest. 

Leibniz  was  in  London  in  1673,  and  from  that  time 
began  to  pay  particular  attention  to  mathematics.  He  was 
in  correspondence  with  Newton,  Oldenburg,  and  others,  on 
questions  connected  with  infinite  series,  and  continued  so 
more  or  less  till  1684,  when  he  published  his  first  ideas  on 
the  Differential  Calculus  in  the  Leipsic  Acts.  But  it  is 
certain  that  Newton  had  been  in  possession  of  the  same 
powers  under  a  different  name,  from  about  1665.  The 
English  philosopher  drops  various  hints  of  his  being  in 
possession  of  a  new  method,  but  without  explaining  what 
it  was,  except  in  one  letter  of  1672,  of  which  it  was  after- 
wards asserted  that  a  copy  had  been  forwarded  to  Leibniz 
in  1676.  Leibniz  published  both  on  the  Differential  and 
Integral  Calculus  before  the  appearance  of  Newton's 
Principia  in  1687  ;  and  indeed,  before  1711,  the  era  of  the 
dispute,  this  new  calculus  had  been  so  far  extended  by 
Leibniz  and  the  Bernoullis,  that  it  began  to  assume  a  shape 
something  like  that  in  which  it  exists  at  the  present  day. 
In  the  first  edition  of  the  Principia^  Newton  expressly  avows 
that  he  had,  ten  years  before  (namely,  about  1677),  in- 
formed Leibniz  that  he  had  a  method  of  drawing  tangents, 
finding  maxima  and  minima,  etc. ;  and  that  Leibniz  had,  in 
reply,  actually  communicated  his  own  method,  and  that  he 
(Newton)  found  it  only  differed  from  his  own  in  symbols. 
This  passage  was,  n5t  very  fairly,  suppressed  in  the  third 
edition  of  the  Principia^  which  appeared  in  1726,  after  the 
dispute  ;  and  the  space  was  filled  up  by  an  account  of 
other  matters.  It  was  obvious  that,  on  the  supposition  of 
plagiarism,  it  only  gave  Leibniz  a  year  to  infer,  from  a  hint 
or  two,  his  method,  notation,  and  results. 

Some  discussion  about  priority  of  invention  led  Dr 
Keill  to  maintain  Newton's  title  to  be  considered  the  sole 
inventor  of  the  fluxional  calculus.  Leibniz  had  asserted 
that  he  had  been  in  possession  of  the  method  eight  years 


OF  LEIBNIZ  185 

before  he  communicated  it  to  Newton.  He  appealed  to 
the  Royal  Society,  of  which  Newton  was  President,  and  that 
body  gave  judgment  on  the  question  in  1712.  Their 
decision  is  now  worth  nothing ;  firstly,  because  it  only 
determined  that  Newton  was  the  first  inventor,  which  was 
not  the  whole  point,  and  left  out  the  question  whether 
Leibniz  had  or  had  not  stolen  from  Newton;  secondly, 
because  the  charge  of  plagiarism  is  insinuated  in  the 
assertion  that  a  copy  of  Newton's  letter,  as  above  mentioned, 
had  been  sent  to  Leibniz.  Now  they  neither  prove  that  he 
had  received  this  letter  in  time  sufficient  to  enable  him  to 
communicate  with  Newton  as  above  described,  or,  if  he  had 
received  it,  that  there  was  in  it  a  sufficient  hint  of  the 
method  of  fluxions.  The  decision  of  posterity  is,  that 
Leibniz  fairly  invented  his  own  method;  and  though 
English  writers  give  no  strong  opinion  as  to  the  fairness 
with  which  the  dispute  was  carried  on,  we  imagine  that 
there  are  few  who  would  now  defend  the  conduct  of  their 
predecessors.  Whoever  may  have  had  priority  of  invention, 
it  is  clear  that  to  Leibniz  and  the  Bernoullis  belongs  the 
principal  part  of  the  superstructure,  by  aid  of  which  their 
immediate  successors  were  enabled  to  extend  the  theory  of 
Newton ;  and  thus  Leibniz  is  placed  in  the  highest  rank  of 
mathematical  inventors. 

The  metaphysics  of  Leibniz  have  now  become  a  by-word. 
He  is  pre-eminent,  among  modern  philosophers,  for  his 
extraordinary  fancies.  His  monads,  his  pre-established 
harmony,  and  his  best  of  all  possible  worlds,  are  hardly 
caricatured  in  the  well-known  philosophical  novel  of 
Voltaire.  If  any  thinking  monad  should  find  that  the  pre- 
established  harmony  between  his  soul  and  body  would 
make  the  former  desire  to  see  more  of  Leibniz  as  a  meta- 
physician, and  the  latter  able  to  second  him,  we  can  inform 
him  that  it  was  necessary,  for  the  best  of  all  possible 
universes,  that  Michael  Hansch  should  in  1728  publish  the 
whole  system  at  Frankfort  and  Leipsic,  under  the  title, 


1 86  CHARACTER    OF  LEIBNIZ 

Leibnitii  Prindpia  philosophica  more  geometrico  demonstrate*  ; 
and  also  that  M.  Tenneman  should  give  an  account  of  this 
system,  and  M.  Victor  Cousin  translate  the  same.  It  is 
not  easy  to  give  any  short  description  of  the  contents,  nor 
would  it  be  useful.  A  school  of  metaphysicians  of  the  sect 
of  Leibniz  continued  to  exist  for  some  time  in  Germany, 
but  it  has  long  been  extinct. 

The  mathematical  works  of  Leibniz  were  collected  and 
published  at  Geneva  in  1768.  His  correspondence  with 
John  Bernoulli  was  also  published  in  1745,  at  Lausanne 
and  Geneva.  It  is  an  interesting  record,  and  exhibits  him 
in  an  amiable  light.  He  gives  his  friend  a  check  for  his 
manner  of  speaking  of  Newton,  at  the  time  when  the 
partisans  of  the  latter  were  attacking  his  own  character, 
both  as  a  man  and  a  discoverer.  He  says,1  "  I  thank  you 
for  the  animadversions  which  you  have  sent  me  on  Newton's 
works ;  I  wish  you  had  time  to  examine  the  whole,  which 
I  know  would  not  be  unpleasant  even  to  himself.  But  in 
so  beautiful  a  structure,  non  ego  paucis  offendar  maculis." 
He  also  says  that  he  has  been  informed  by  a  friend  in 
England,  that  hatred  of  the  Hanoverian  connexion  had 
something  to  do  with  the  bitterness  with  which  he  was 
assailed;  "Non  ab  omni  veri  specie  abest,  eos  qui  parum 
Domui  Hanoveranae  favent,  etiam  me  lacerare  voluisse; 
nam  amicus  Anglus  ad  me  scribet,  videri  aliquibus  non  tarn 
ut  mathematicos  et  Societatis  Regise  Socios  in  socium,  sed 
ut  Toryos  in  Whigium  quosdam  egisse."  2 

1  Ibid.,  vol.  ii,  p.  234. 

2  Ibid.,  p.  321. 


APPENDIX  II.   TO  THE  THIRD  ESSAY 

(See  note  I  on  p.  154.) 

NOTE  BY  DE  MORGAN  ON  THE  CHARACTER  OF  NEWTON 
AND  ON  THE  ACTIONS  OF  THE  ROYAL  SOCIETY.1 

RECENT  knowledge  has  recoloured  the  mythical  portrait  of 
Newton's  character.  He  was  not  a  simple-minded  man  in 
the  sense  propounded :  he  was  not  like  the  old  philosopher 
who  knocked  his  foot  against  a  stone  while  he  was  looking 
at  the  stars.  Though  not  learned  in  human  nature,  he  was 
very  much  the  man  of  the  world.  He  stuck  to  the  main 
chance,  and  knew  how  to  make  a  cast.  He  took  good  care 
of  his  money,  and  left  a  large  fortune,  though  very — even 
magnificently — liberal  on  suitable  occasions,  especially  to 
his  family.  He  was  observant  of  small  things,  as  are  all 
men  of  suspicious  temperament;  and  he  had  a  strong 
hatred  of  immorality,  whether  in  word  or  deed,  which  no 
doubt  would  have  turned  his  acuteness  of  observation,  and 
his  tendency  to  suspicion,  upon  anything  from  which  infer- 
ence could  have  been  drawn.  Those  who  imagine  that 
Newton  was  always  thinking  of  gravitation  might  just  as 
well  imagine  that  Wellington  was  always  thinking  of 
strategy.  The  following  description  applies  to  both.  After 
this  (the  Prindpia  or  Waterloo,  according  to  the  person 
thought  of),  he  lived  about  forty  years,  during  which  his 
attention  to  what  had  been  his  main  pursuit  was  inter- 

1  [This  Appendix  is  extracted  from  De  Morgan's  book,  Newton : 
his  Friend:  and  his  Niece  (London,  1885,  the  first  paragraph  on 
pp.  70-71,  and  the  rest  on  pp.  130-136),  which  was,  for  the  most  part, 
written  in  1858  (see  note  I  on  p.  171).] 

187 


1 88  ON  NEWTON  AND 

mittent  and  casual,  and  rather  directive  of  others  than 
executive.  He  had  a  new  career  before  him,  in  which 
again  he  was  eminently  successful ;  and  in  the  last  years  of 
his  life  he  was  of  all  his  contemporaries  the  most  famous 
and  the  most  respected. 

It  was  in  Britain  the  temper  of  the  age,  before  Baily's 
Life  of  Flamsteed  rudely  broke  in  upon  the  illusion,  to  take 
for  granted  that  Newton  was  human  perfection.  There  is 
a  class  in  this  country  which  has  a  perennial1  existence 
among  all  that  is  middle,  from  nobility  down  to  handicraft ; 
into  both  of  which  it  throws  its  shoots.  It  is  a  respectable 
class :  it  can  truly  be  described  as  so  respectable,  you  can't 
think  !  It  is  a  useful  class ;  it  is  part  of  the  ballast  of  our 
good  ship ;  and  though  our  middle  ranks  furnish  a  much 
larger  percentage  of  that  which  is  ballast  and  cargo,  both, 
yet  no  ballast  is  useless.  Who  does  not  know  the  smug 
individual  of  this  species,  as  he  sees  him  picking  his  way 
through  the  world  ?  His  highest  model  is  aristocracy ;  his 
social  life  is  silver-forkery ;  his  main  pursuit  is  money- 
grubbery ;  and  his  whole  religion  is  Sunday-prayery.  This 
is  the  complete  specimen,  fit  for  the  museum ;  but  the 
characteristics  are  variously  interfused  through  an  immense 
mass,  often  lost  in  other  and  better  features,  except  to  a 
close  observer.  This  class  is,  in  every  case  in  which  its 
members  knew  the  name  of  Newton,  the  one  in  which  you 
were  safe  to  be  reckoned  as  in  the  broad  way  if  you  imputed 
anything  wrong  to  the  man  who  bore  that  name  at  the 
Mint — a  position  which  was  mysteriously  connected  with 
wonderful  discoveries  in  the  heavens. 

"  And,  so  you  think  that  Newton  told  a  lie  ; 
Where  do  you  hope  to  go  to  when  you  die  ?  " 

By  help  of  this  class,  without  which  the  man  of  science 
could  not  have  put  Newton  on  the  pedestal  which  had  been 
made  for  him,  it  was  practicable  to  allow  what  had  the 

1  ["  Percential ''  is  misprinted  in  the  original.] 


THE  ROYAL   SOCIETY  189 

clearest  appearance  of  a  direct  and  deliberate  falsehood  on 
Newton's  part  to  stand  unexamined  for  more  than  a  century. 
Newton,  in  his  final  conflict  with  Leibniz,  declared  that  the 
decision  at  the  Royal  Society  against  Leibniz  had  been 
voted  by  a  "  numerous  committee  of  gentlemen  of  different 
nations."  The  world  was  never  told  of  more  than  six,  all 
British  subjects  of  English  mother-tongue;  no  list  of  the 
committee  was  published  with  the  decision.  Here  was,  to 
all  appearance,  if  not  a  falsehood,  worse — the  evasion  of 
calling  the  English,  Scotch,  etc.,  different  nations  in  refer- 
ence to  a  dispute  between  Britain  and  the  Continent.  If 
the  faith  in  Newton  had  been  anything  but  a  formula,  some 
would  have  reasoned  thus: — " Newton  could  not  be  false  : 
he  says  the  committee  had  members  of  different  nations ; 
let  us  look  at  the  minute-books  of  the  Royal  Society,  and 
find  them  out."  But  this  was  not  thought  necessary.  I 
had  long  been  puzzled  with  this  statement  of  Newton's ; 
though  I  knew  him  to  be  capable  of  being  betrayed  by  the 
necessities  of  his  case  into  that  culpable  evasion  in  which 
self-love  finds  excuse,  I  did  not  believe  that  his  principles 
would  allow  him  directly  and  wilfully  to  falsify  a  fact ;  or 
that  his  acuteness  would  allow  him  to  do  it  on  so  small  a 
matter  and  to  so  little  purpose.  It  chanced  to  me,  in 
1845,  to  look  at  a  Life  of  De  Moivre  of  the  rarest  character, 
by  his  friend  Dr  Matthew  Maty,  Sec.,  R.S.  I  never  saw 
more  than  one  separate  copy ;  but  I  long  afterwards  found 
it  in  the  Journal  Britannique  for  1755 — a  French  journal, 
published  in  England  by  the  "little  black  dog,"  as  Sam 
Johnson  called  him — Maty  himself.  Here  I  found  eleven 
members  named,  two  of  them  aliens — De  Moivre  himself 
and  Bonet  the  Prussian  minister.  And  though  they  were 
the  only  two  foreigners,  yet  De  Moivre  was  a  host:  the 
only  one  among  the  rest  who  was  fit  to  stand  up  against 
him  for  one  moment  on  a  mathematical  question  was 
Halley.  On  application  to  the  Royal  Society,  the  facts 
were  verified  immediately :  the  six  who  have  passed  for  the 


190  ON  NEWTON  AND 

whole  were  those  first  appointed ;  the  remaining  five  were 
added  piecemeal  in  the  five  weeks  following  the  first 
nomination. 

I  drew  up  a  few  words  on  this  discovery,  and  sent  them 
to  the  Royal  Society.  I  thought  they  would  be  a  charta 
volans  for  the  Proceedings,  etc.  To  my  very  great  surprise 
they  were  printed  in  all  the  dignity  of  the  Philosophical 
Transactions,  in  which  no  historical  paper  has  ever  appeared, 
that  I  know  of — certainly  none  within  the  century.  But 
the  matter  concerned  the  character  of  Newton.  The  little 
bit  of  two  and  three-quarter  pages,  with  the  facts  about  the 
Committee  and  some  anecdote — as  how,  for  instance, 
Newton  said  nothing  but  his  age  prevented  him  from 
having  "another  pull  at  the  moon" — looks  curious  among 
the  elaborate  mathematical  and  physical  papers.  This  is  so 
far  a  mere  anecdote :  it  takes  meaning  in  connexion  with 
what  follows. 

About  a  year  after  the  preceding  paper  was  sent,  some  of 
those  accidents,  by  which  those  who  are  prepared  can  snap 
surmises,  as  well  as  facts,  led  me  to  a  surmise  that  perhaps 
the  reprint  (1722)  of  the  Commercium  Epistolicum  (1712) — 
as  the  work  containing  the  reasons  and  decisions  of  the 
above-named  Committee  is  called — had  not  been  quite 
fairly  made.  I  say  reprint,  not  second  edition  ;  for  the  very 
title-page  was  reprinted  with  the  old  date,  after  the  avowedly 
new  matter  and  a  new  title  over  all,  which  amounted  to  the 
most  positive  declaration  that  not  a  comma  was  intentionally 
changed.  I  had  no  copy  of  the  first  edition,  so  I  applied  to 
the  Council  of  the  Royal  Society  for  the  loan  of  their  copy, 
stating  why  I  wanted  it  The  request  was  instantly  granttd ; 
and  I  found,  on  examination,  that  some  alterations  had  been 
made,  of  which  some  were  decidedly  unfair  in  matter,  all 
being  of  course  unjustifiable  under  the  old  date  and  without 
notice.  The  worst  among  them  was,  that  whereas  the  old 
Committee  did  not -say  precisely,  in  the  evidence,  when  the 
letter  on  which  the  most  depended  was  forwarded  to  Leibniz, 


THE  ROYAL   SOCIETY  \gi 

a  date  for  this  transmission  was  foisted  into  the  reprint.  It 
ought  to  be  said  that  the  notions  of  the  literary  world,1  in 
that  day,  about  the  sanctity  of  documents  were  by  no  means 
so  rigid  as  they  are  now ;  so  that  what,  done  by  one  of  us, 
would  be  sheer  rascality,  may  be  let  off  with  a  much  softer 
name.  I  drew  up  an  account  of  the  alterations,  and  sent 
it  to  the  Royal  Society ;  to  have  sent  it  elsewhere  would 
have  been  to  say,  in  effect,  that  though  I  knew  the  Society 
would  go  out  of  the  way  to  clear  the  fame  of  Newton,  I 
could  not  trust  them  to  clear  their  own  wrong  to  Leibniz. 
That  they  had  some  hand  in  it  was  clear  from  the  reprint 
having  cuts  from  the  old  wood  blocks  which  were  the 
property  of  the  Society.  The  Society  proved  itself  worthy 
of  the  reflection  which  I  could  not  venture  to  cast;  it 
declined  to  print  the  second  paper.  I  gathered  that  the 
council  thought  it  would  be  necessary  to  submit  my  paper 
and  the  documents  to  a  special  committee  of  examination. 
The  documents  were  two  printed  books,  and  the  question 
was  whether  certain  passages  in  one  book  were  accurate 
reprints  of  certain  passages  in  the  other ;  and  if  not,  how 
they  differed.  I  have  no  doubt  the  real  reason  was,  that  in 
the  paper  was  seen  danger  of  danger  to  Newton's  character. 
I  afterwards  saw  a  published  reason,  of  which  I  was  not 
cognisant  at  the  time,  for  .thinking  that  Newton  himseli 
was  the  editor  of  this  reprint,  and  the  writer  of  the  preface 
which  preceded  the  old  title.  Sir  D.  Brewster,  from  the 
"  Portsmouth  Papers,"  found  that  I  was  quite  right.  When 
I  made  this  last  discovery,  it  crossed  my  mind  for  one 
moment  that  the  fact  was  known  in  the  Council  of  the 
Royal  Society,  and  the  refusal  to  investigate  the  question 
was  in  part  the  consequence  of  disinclination  to  bring  it 
out.  But  this  notion  took  no  root;  I  soon  felt  satisfied 
that,  whatever  unconscious  bias  might  do,  there  was  no 
reason  to  fear  a  definite  intention  to  suppress  a  definite 
fact.  And  further,  so  small  and  so  inexact  is  the  know- 
1  ["Word"  is  misprinted  in  the  original.] 


192  ON  NEWTON  AND 

ledge  of  the  history  of  science  among  scientific  men,  that 
I  could  easily  imagine  not  one  single  person  on  the  council 
knew  so  much  as  that  there  had  been  a  reprint,  much  less 
that  Newton's  active  share  in  the  reprint  had  been  matter 
of  discussion,  of  affirmation,  and  denial. 

I  applied  for  permission  to  withdraw  the  paper,  hoping 
thus  to  nullify  the  proceedings  in  form  at  least.  But  the 
laws  of  the  Society  prevent  the  withdrawal  of  any  communi- 
cation which  has  undergone  adjudication ;  hence  this  little 
matter  must  have  its  little  place  in  the  history  of  the 
Society,  and  its  somewhat  larger  place  in  mine.  A  copy 
would  have  been  allowed  me  if  I  had  requested  it ;  but  I 
preferred  to  write  another  paper,  and  to  request  its  insertion 
in  the  Philosophical  Magazine  (June,  1848). 

One  testimony  to  the  significance  of  the  variantes  is  that 
of  Sir  D.  Brewster,  who  holds  it  wise  to  omit  all  mention  of 
them.  After  my  paper,  which  I  took  care  he  should  have, 
and  with  full  knowledge  of  the  new  work  being  reprinted 
under  the  old  date>  he  calls  it  "  a  new  edition  with  notes,  a 
general  review  of  it  and  a  preface  of  some  length."  x  He 
did  not  even  give  the  true  date  (1722),  but  sticks  by  that 
of  the  second  title-page  (1725).  This  is  of  some  conse- 
quence; for  three  years,  at  Newton's  age,  then  made  a 
difference  in  the  palliation  which  years  and  infirmity  may 
be  made  to  give.  But  it  must  be  remembered  that  persons 
unused  to  bibliography  are  often  not  even  aware  of  the 
distinction  between  a  reprint  and  a  new  edition. 

I  freely  and  unreservedly  blame  the  Council  of  the  Royal 
Society — collectively,  of  course — for  not  printing  the  account 
of  the  variations  mentioned  above ;  they  missed  a  golden 
opportunity.  They  might  have  shown  that  the  beautiful 
edition  of  the  Commercium  Epistolicum,  published  in  1856, 
by  Biot  and  Lefort,  at  the  expense  of  the  French  Govern- 
ment, "avec  1'indication  des  variantes  de  1'edition  de  1722," 
would  have  recorded  that  these  variantes  were  first  made 
1  [Brewster,  Memoir s>  1855,  vol.  ii,  p.  75.] 


THE   ROYAL    SOCIETY  193 

\ 

known  by  the  Royal  Society  itself,  the  body  which  was 
most  concerned  in  the  publication  of  them.  Considered  as 
an  act  of  reparation,  the  opportunity  is  lost,  and  the  revela- 
tions of  the  "Portsmouth  Papers"  and  of  those  of  Leibniz 
have  left  little  chance  of  another.  The  Royal  Society,  in 
this  matter,  reminds  one  much  of  those  old  managers  of  the 
impeachment,  who,  when  Warren  Hastings,  many  and 
many  a  year  after  his  acquittal,  appeared  before  a  House 
of  Commons,  the  members  of  which  rose  and  uncovered  at 
his  retirement,  remained  sitting  with  their  hats  on,  to  show 
their  sullen  consistency.  As  a  question  of  curiosity,  I 
asked  myself  whether  Leibniz  ever  found  as  stubborn  an 
adherent  in  spite  of  all  that  could  be  learnt?  I  could  not 
remember  such  a  thing  in  real  life,  but  the  optimist  of 
Voltaire's  fiction  hits  the  case  exactly :  "  *  Eh  bien !  mon 
cher  Pangloss,'  lui  dit  Candide,  'quand  vous  avez  e*te 
pendu,  disseque,  roue  de  coups,  et  que  vous  avez  rame  aux 
galeres,  avez-vous  toujours  pense  que  tout  allait  le  mieux  du 
monde?'  'Je  suis  toujours  de  mon  premier  sentiment,' 
repondit  Pangloss ;  'car  enfin  je  suis  philosophe;  il  ne  me 
convient  pas  de  me  dedire.  Leibnitz  ne  pouvant  pas  avoir 
tort.  , 


1.3 


INDEX 


Achilles,  120. 
Adams,  J.  C.,  6,  21,  105. 
Addison,  178. 
Anne,  Queen,  35. 
Antitrinitarian,  55,  58,  59. 
Arabians,  107. 
Arbuthnot,  27. 
Archimedes,  23,  107,  121. 
Ariam'sm,  54,  55,  57,  176. 
Arians,  vii,  53,  56,  172,  176. 
Aristides,  180. 
Aristotle,  48. 

Arithmetic,  universal,  13,  16. 
Aston,  Francis,  27,  132,  134. 
Athanasius,  176. 
Atticus,  122. 

Babbage,  Charles,  157. 
Bacon,  Francis,  128,  180. 
Baily,  Francis,  v,  40,  143,  188. 
Ball,  W.  W.  Rouse,  4,  7,  13,  19, 

20,  23,  103. 
Baptists,  55. 

Barbara  (syllogism),  130. 
Baron,  Richard,  55,  58,  172. 
Barrow,  Isaac,  9,   II,  12,  24,  29, 

73,   83,   104,  107,   109,  1 10, 

112,  131. 
Barton,  Catherine,  6,  34,  160  ff., 

178. 

Colonel,  6,  166. 
Robert,  6. 

Beman,  W.  W.,  103. 
Bentley,  Richard,  15,  1 6. 
Bernoulli,  James,  72. 
John,  28,  30,  32,  33,  72,  101, 

112,  186. 
Nicolaus,  72. 
Bernoullis,  the,  26,  72,  88,  107, 

179,  184. 


Binomial  Theorem,  24,  25. 
Biot,   Jean    Baptiste,   ix,    3,    58, 

123,   192. 

Blount,  Martha,  171. 
Bohn,  Henry  G  ,  v. 
Bonet,  27,  189. 
Boreili,  18. 
Boswell,  James,  133. 
Bouillaud,  18,  52. 
Boyle,  Robert,  15. 
Bracegirdle,  Mrs,  171. 
Bradley,  James,  183. 
Brahe,  Tycho,  18. 
Brewster,  Sir  David,  ix,  xiii,  3,  5, 

6,  7,  8,  10,  n,  12,  15,  17,  is. 

34,   43,   44,  56,  58,  68,  85, 

104,  107,  108,  109,  no,  115, 

117,  119,  122,  124,  125,  127, 
128,  131,  132,  134,  135,  138, 
139,  141,  142,  143,  144,  146, 
147,  148,  ISO,  154,  155,  156, 

158,  160,  161,  162,  163,  164, 
165,  166,  167,  168,  169,  170, 
171,  172,  176,  177,  178,  191, 
192. 

Brill,  A.,  109. 

Brougham,  Lord,  3. 

Brunschvicg,  Leon,  106. 

Burgess,  Bishop,  60. 

Burnet,  27. 

Csenopolis,  121. 
Cajeti  (syllogism),  130. 
Calculus,  differential,  23   ff.,   71, 

94,  95  ff- 
Cambridge,    University  of,  6,  9, 

10,  13. 

Candide,  193. 
Cantor,    Moritz,    viii,    103,    107, 

109,  no,  112,  114. 


194 


INDEX 


195 


Cassini,  42. 

Cavalieri,   Bonaventura,  96,    107, 

121,  146. 

Cdarent  (syllogism),  130. 
Chalmers,  Dr,  57. 
Chamberlayne,  86. 
Charles  II.,  13. 
Cheyne,  Dr,  89,  96. 
Christianity.    Newton     and,    vii, 

53  ff- 
Cipher,  Newton's  fluxional,  25  fF., 

93,  157- 

Clairaut,  Alexis  Claude,  61,  179. 
Clarke,  Samuel,  43,  55,  59. 
Cobbett,  128. 
Collins,  John,   12,  24,  28,  29,  31, 

70,    7i,    72,  73»  74,  75,  78, 

79,  80,    82,  83,  84}  85,  87, 
106,  109,  no,  in,  152,  158, 

159- 

Colson,  John,  1 10. 
Commerchtm     Epistolicum,    viii, 

28,   39,   68,  71,  75,  78,  79, 

80,  82,   87,    115,    152,    153, 

154,  I56>  J57,  190,  192. 
Committee  of  Royal  Society,  27, 

68,  100,  153  ff.,  190. 
Conduitt,  5,  6,  130,  131,  141,  163, 

164,  165,  177,  178. 
Mrs,  178. 
Congreve,  171. 
Conti,  Abbe,  30,  31,  33,  77,  106, 

156. 

Copernicus,  139. 
Cotes,    Roger,    3,   6,  35,  73,  74, 

96,  104. 

Cousin,  Victor,  186. 
Covel,  Dr,  133. 
Cowper,  171. 

Craig,  John,  88,  89,  96,  151. 
Crompton,  Samuel,  xi. 
Cromwell,  H.,  167. 

Oliver,  129. 
Curvity,  radius  of,  1 1. 
Cyprian,  58. 


Dafenes  (syllogism),  130. 
Daniel,  prophecies  of,  16,  53. 
Dary,  Michael,  no. 
Delambre,  183. 


I   De  Moivre,  Abraham,  27,  50,  89, 

96,  189. 
J   De  Morgan,  Augustus,  v,  vi,  vii, 

viii,  ix,  x,  xiii,  3,  II,  21,  34, 

48,  63,  68,  96,  101,  102,  104, 

108,  154,  156,  158,  160,  162, 

167,  1 68,  169,  171,  177,  183, 

187. 
Mrs,  v,  vi,  vii,  ix,  21,  37,  104, 

148,  171,  183. 
Descartes,  Rene,   10,   11,  18,  24, 

37,    61,   107,  112,  113,  128, 

I3i>  183. 

Diamond,  Newton's  dog,  14. 
Diana,  169. 
Differential  Calculus  (see  Calculus 

and  Fluxions). 
Dollond,  183. 
Duillier,  Fatio  de,  27,  96,  112. 

Edleston,  J.,  3,   7.   9,  12,  13,  35, 
42,  73>  77,  78,  104,  108,  109, 

IIO,   III,   112,   114,   131. 

Ekins,  Dr,  16. 

Erasmus,  58. 

Euclid,  9,  10,  n,  107,  127,  128. 

Euler,  Leonhard,  107,  183. 


Fecana  (syllogism),  130. 
Fermat,  Pierre  de,  29,   107,  112, 

121,  146. 
Fink,  Karl,  103. 
"Firstrede,  Prof.,"  121. 
Flamsteed,   John,   v,  39,  40,  41, 

42,    43,   104,   143,   141,   155, 

159,  1 88. 
Fluxional    controversy,    viii,  xiii, 

27  ff.,  67  ff.,  U4ff.,  144  ff. 
Fluxions,  vii,  n,  16,  23  ff.,  67  ff. , 

89,  130,  149. 
Fontenelle,  3,  5,  6. 
French  Academy,  78. 


Gadaco  (syllogism),  1 30. 
Galileo,  18,  123. 
Galloys,  72. 
George  I.,  31,  35. 
George  II.,  35. 
George,  Prince,  143. 


INDEX 


Gerhardt,  Carl  Immanuel,  vii,  67, 

71,72,96,97,  102,  105,  106, 

114,  115. 

Giordano,  Vitale,  72. 
Glendower,  157. 
Gordon,  Thomas,  55. 
Grandi,  Guido,  72. 
Gravitation,   Newton's  theory  of 

universal,  18  ff,  51-53,  138  ff. 
Gray,  G.  J.,  x,  3,  7,  16,  103,  105, 

109,  no,  115. 
Gregory,  James,  5,  29,  70,  72,  73, 

74,  75,  78,  79,  83,  1 10. 
Guhrauer,  G.  E.,  106. 

Hales,  95. 

Halifax,  Earl  of,  6,  34,  160  ff. 

Halley,  Edmund,  21,  22,  23,  27, 

38,  41,  48,  50,  96,   138,  139, 

141,  183,  189. 
Hansch,  Michael,  185. 
Harris,  John,  90,  96. 
Harrison,  183. 
Hastings,  Warren,  193. 
Hayes,  Charles,  90,  91,  96. 
Haynes,  Hopton,  55,  57,  58,  172, 

176. 

Hebare  (syllogism),  130. 
Hector,  122. 
Hercules,  120. 
Herschel,  W.,  183. 
Hill,  27. 
Homer,  179. 
Hooke,   Robert,    17,  18,  20,  22, 

23.  139- 

Hopital,  de  1',  48,  72,  88,  89,  90, 

91. 

Horace,  125. 
Horsley,  Samuel,  15,  16,  54,  57, 

58,   108,   109,   172. 
Hudde,  73,  85,  87,  107,  146,  160. 
Humanitarians,  vii,  53,  55,  176. 
Hutton,  Charles,  69,  95. 
Huygens,  Christian,  x,  15,  18,  19, 

72,  107. 

Infinite  Series,  Method  of,  n. 
Infinitesimal    Calculus    (see    also 

Calculus  and  Fluxions),  vii. 
Infinitesimal     view    of    fluxions, 

89  ff. 


Jacobites,  30. 
James  I.,  5. 
James  II. ,  13,  133. 
Jerome,  57. 
Johnson,  Samuel,  189. 
Jones,  Sir  W.,  27,  108, 
Jupiter,  123. 
Juvenal,  125. 

Kaleidoscope,  123. 

Keill,  John,  vii,  27,  28,  79,  87, 

154- 

Kepler,  9,  18,  19,  107. 
Kinckhuysen,  107,  109,  in. 
Kirmansegger,  Baron,  30. 
Knight,  Charles,  v,  67,  171,  183. 
Kowalewski,  Gerhard,  no,  114. 

Lagrange,  Joseph  Louis,  107,  183. 

Laplace,  179,  183. 

Le  Clerc,  58,  60. 

Lefort,  192. 

Leibniz's  character,  151,  183  ff. 

Leibniz,  Gottfried  Wilhelm,  v, 
vii,  viii,  ix,  x,  xiii,  24,  25,  26, 
27,28,29,  30.31,32,34,35, 
39,  40,  44,  49,  68,69,70,71, 
72,  73,  74,  75,76,77,78,  79, 
80,  81,  82,  84,85,  86,87,  88, 

89,  9i,  92,  93,  94,  95,  96,  97, 
98,  99,  100,  101,  102,  103, 
106,  107,  in,  112,  113,  114, 

115,   121,    143,   144,   145,   I46, 

147, 148, 149,  150, 151, 152, 

157,  159,  160,  179,  183,  184, 
185,  186,  189,  190,  191,  193. 

manuscripts  of,  67,  96  ff.,  1 12  ff. 

metaphysics  of,  185. 
Le  Verrier,  U.  J.  J.,  21. 
Liveing,  G.  D.,  6,  105. 
Locke,  John,  35,  46,  58,  59,  182. 
Lowthorp,  J.,  84. 
Luard,  H.  R.,  6,  105. 
Lymington,  Viscount,  6. 
Lynn,  W.  T.,  3. 

Macaulay,     Thomas  ]  Babington, 

8^171. 

Macclesfield,  Earl  of,  83,  104. 
Mach,  Ernst,  4,  19. 
Machin,  27. 


INDEX 


197 


Maclaurin,  107. 
Martin,  Benjamin,  3. 
Mary,  Queen,  133. 
Maskelyne,  183. 
Maty,  Matthew,  189. 
M'Cormack,  T.  J.,  4. 
Mercator,  Nicolas,  107. 
Middle  Ages,  107. 
Montague,  Charles  {see  also  Hali- 
fax), 34,  1 60,  167. 
Motte,  Andrew,  16. 
Mouton,  Gabriel,  69. 

Napoleon,  181. 

Newton,  Sir  Isaac,  v,  vi,  vii,  viii, 

ix,  x,  xi,  xiii,  68,  69,  70,  72, 

73,   74,   75,   77,'  78,  79,  80, 

81,   82,  83,   84,  85,  87,  88, 

89,   90,  91,   92,  93,  94,  96, 

97,  100,  102,  103,  104,  105, 

106,  1 08,  109,  no,  in,  112, 

113,  114,  115,  184,  185,  186. 

biography  of,  3-63,  119-182. 

character    of,    4,    36   ff.,    134, 

156  ff.,  i8off.,  187  ff. 
Isaac,  his  father,  4. 
John,  5. 

manuscripts  of,  viii,  7,  67,  107  ff. 
religious  beliefs  of,  vi,  171  ff. 
theological  writings  of,  53  ff. 
Nieuwentiit,  107. 
Noether,  M.,  109. 
Norris,  Lady,  177,  178. 

Oldenburg,    Henry,   24,    25,    27, 

29,  32>  70,   71,   73,   74,  78, 
79,    81,   89,   92,    100,    106, 
no,  in,  152,  184. 
Optics,  Newton's  work  on,  16  ff., 
43,  137- 

Paget,  22. 

Pangloss,  193. 

Pappus,  107. 

Pascal,  Blaise,  107,  112. 

Peacock,  George,  138. 

Pemberton,    Henry,    36,    40,  43, 

1 10,  131,  159. 
Pepys,  Samuel,  133. 
Pericles,  122. 
Pertz,  G.  H.,  72. 


Picard,  26. 
Pilkington,  6. 
Pope,  Alexander,  167,  171. 
Portsmouth,  Earl  of,  6,  105,  154. 
Portsmouth   Papers,  6,    54,    125, 
126,  135,  154,  156,  172,  191, 

193- 
Pound,  43. 
Priestley,  Joseph,  57. 
Principia,    Newton's,    9,    15,   16, 

18,    22,   23,  26,   31,  32,  33, 

34,  35,  36,  39,  4i,  43,  5°, 
60,  61,  88,  89,  96,  104,  128, 
13°,  131.  !32,  138,  140,  148, 
IS1.  !52,  155,  159,  164,  172, 
1 80,  187. 
Pryme,  de  la,  14. 

Ranyard,  A.  C.,  171. 

Raphson,  Joseph,  31,  69,  93,  102, 
103,  108,  109,  149. 

Renascence,  107. 

Ricci,  83. 

Rigaud,  Stephen  Jordan,  104. 
Stephen   Peter,    4,  20,  94,  96, 
97,  102,  103,  104,  108. 

Robarts,  27. 

Roberval,  G.  P.,  107. 

Robins,  109. 

Romulus,  122. 

Rosenberger,  Ferdinand,  4,  15, 
17,  18,  27,  105,  107,  109, 
no,  112,  114. 

Royal  Society,  vii,  ix,  x,  xiii,  7, 
15,  16,  17,  20,  22,  24,  27, 
28,  35,  38,  41,  44,  47,  54, 
56,  68,  70,  71,  74,  75,  77, 
81,  84,  86,  89,  100,  112, 

135,  i36'  !39,  H7,  153,  156, 
160,  186,  187,  189,  190,  191, 
192,  193. 

Sanderson,  9,  129. 
Sangrado,  132. 
Sardica,  Council  of,  176. 
Schooten,  F.  van,  n,  107. 
Scott,  Sir  Walter,  181. 
Scriven,  E.,  x. 
Shakspere,  119. 
Sharp,  Abraham,  v. 
Sherlock,  59. 


198 


INDEX 


Sloman,  H.,  115. 

Sluse,  73,  81,  82,  83,  84,  85,  87, 

98,  107,  no. 
Smith,  Barnabas,  5. 

David  Eugene,  103. 

Hannah,  6. 
Socinians,  vii,  53. 
South,  Sir  James,  59. 
Stella,  1 68. 

Stewart,  John,  109,  1 10. 
Stokes,  G.  G.,  6,  105. 
Storey,  Miss,  7,  22,  178. 
Stourbridge  fair,  q. 
St.  Vincent,  Gregory  of,  107,  112. 
Subsizar,  8. 
Suisset,  130. 
Swift,  Jonathan,  43,  168,  169. 

Tangents,  drawing  of,  n. 
Taylor,  Brook,  107. 
Teignmouth,  Lord,  108. 
Tenneman,  186. 
Thomson,  Dr,  54. 
Torricelli,  E.,  107. 
Tracts,  Unitarian,  54. 
Trinitarians,  vii,  53,  57,  58,  59. 
Trinity  College,  Cambridge,  6,  8, 

121,  127,  164. 
Tschirnhaus,  E.  W.  von,  72,  74, 

79,  1 06,  in,  113. 
Tumor,  Edmund,  5,  7. 


Unitarians,    53,  55,  57,  59,  172, 

173- 

Unwin,  Mrs,  171. 
Uranus,  21. 
Uvedale,  Robert,  11. 

Valerius,  107. 
Vanderbank,  x. 
Varignon,  Pierre,  72. 
Vieta,  ii. 
Vincent,  Dr,  22. 
Voltaire,  160,  185,  193. 

Wallis,  John,  n,  12,  24,  26,  59, 
72,  82,  85,  89,  90,  91,  92  tf., 
104,  107,  1 10,  in,  121,  157. 

Wallop,  6. 

Ward,  Seth,  13. 

Weissenborn,  Hermann,  105,  ii_). 

Weld,  68,  86. 

Wellington,  Duke  of,  181,  187. 

Wetstein,  58. 

Whiston,  William,  v,  13,  35,  39, 
44,  55,  56,  57,  59,  172,  176. 

William  III.,  King,  43,  53,  133. 

Wilson,  109. 


Young,  Thomas,  137,  138. 
Zendrini,  J2. 


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